• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-21
Yuhua Sun, Tongjiang Yan, Qiuyan Wang

In 2008, a class of binary sequences of period $$N=4(2^k-1)(2^k+1)$$ with optimal autocorrelation magnitude has been presented by Yu and Gong based on an m-sequence, the perfect sequence (0, 1, 1, 1) of period 4 and interleaving technique. In this paper, we study the 2-adic complexity of these sequences. Our result shows that it is larger than $$N-2\lceil \mathrm {log}_2N\rceil +4$$ (which is far larger

更新日期：2021-01-21
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-19

In this paper, we propose three new turn-based two player roulette games and provide positional winning strategies for these games in terms of depths of words over finite commutative rings with unity. We further discuss the feasibility of these winning strategies by studying depths of codewords of all repeated-root $$(\alpha +\gamma \beta )$$-constacyclic codes of prime power lengths over a finite

更新日期：2021-01-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-19
Zhongxiao Wang, Qunxiong Zheng, Xiaoxin Zhao, Xiutao Feng

Nonlinear feedback shift registers (NFSRs) are important building blocks for stream ciphers. The cascade connection of an n-stage full-length linear feedback shift register (LFSR) into an m-stage NFSR is called a Grain-like structure. In this paper, we focus on Grain-like structures which can generate minimal and maximal possible period sequences. The existence of Grain-like structures which can generate

更新日期：2021-01-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-19
José Andrés Armario, Ivan Bailera, Ronan Egan

Codes from generalized Hadamard matrices have already been introduced. Here we deal with these codes when the generalized Hadamard matrices are cocyclic. As a consequence, a new class of codes that we call generalized Hadamard full propelinear codes turns out. We prove that their existence is equivalent to the existence of central relative (v, w, v, v/w)-difference sets. Moreover, some structural properties

更新日期：2021-01-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-19
Makoto Araya, Masaaki Harada, Ken Saito

Linear complementary dual (LCD) codes are linear codes that intersect with their dual trivially. We give a characterization of LCD codes over $$\mathbb {F}_q$$ having large minimum weights for $$q \in \{2,3\}$$. Using the characterization, for arbitrary n, we determine the largest minimum weights among LCD [n, k] codes over $$\mathbb {F}_q$$, where $$(q,k) \in \{(2,4), (3,2),(3,3)\}$$. Moreover, for

更新日期：2021-01-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-17
Sascha Kurz, Eitan Yaakobi

In this work private information retrieval (PIR) codes are studied. In a k-PIR code, s information bits are encoded in such a way that every information bit has k mutually disjoint recovery sets. The main problem under this paradigm is to minimize the number of encoded bits given the values of s and k, where this value is denoted by P(s, k). The main focus of this work is to analyze P(s, k) for a large

更新日期：2021-01-18
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-17
Tran van Trung

An extending theorem for s-resolvable t-designs is presented, which may be viewed as an extension of Qiu-rong Wu’s result. The theorem yields recursive constructions for s-resolvable t-designs, and mutually disjoint t-designs. For example, it can be shown that if there exists a large set LS[29](4, 5, 33), then there exists a family of 3-resolvable 4-$$(5+29m, 6, \frac{5}{2}m(1+29m) )$$ designs for

更新日期：2021-01-18
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-16
James A. Davis, J. J. Hoo, Connor Kissane, Ziming Liu, Calvin Reedy, Kartikey Sharma, Ken Smith, Yiwei Sun

A $$(v,k,\lambda )$$ symmetric design is said to have the symmetric difference property (SDP) if the symmetric difference of any three blocks is either a block or the complement of a block. The designs associated to the symplectic difference sets introduced by Kantor (J Algebra 33:43–58, 1975) have the SDP. Parker (J Comb Theory Ser A 67:23–43, 1994) claimed that the symplectic design on 64 points

更新日期：2021-01-18
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-16
Nicholas J. Cavenagh, Adam Mammoliti, Ian M. Wanless

A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type $$(n;\lambda )$$ if it contains $$n/\lambda$$ symbols, each of which occurs $$\lambda$$ times per row and $$\lambda$$ times per column. In the case when $$\lambda =n/2$$ we refer to the frequency square as binary. A set of k-MOFS$$(n;\lambda )$$ is a

更新日期：2021-01-18
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-12
Hiram H. López, Beth Malmskog, Gretchen L. Matthews, Fernando Piñero-González, Mary Wootters

In this paper, we construct codes for local recovery of erasures with high availability and constant-bounded rate from the Hermitian curve. These new codes, called Hermitian-lifted codes, are evaluation codes with evaluation set being the set of $${{\mathbb {F}}}_{q^2}$$-rational points on the affine curve. The novelty is in terms of the functions to be evaluated; they are a special set of monomials

更新日期：2021-01-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-11
Stefano Innamorati, Fulvio Zuanni

In this paper we remove the solid incidence assumption in the characterization of J. Schillewaert (A characterization of quadrics by intersection numbers, Des. Codes Cryptogr., 47 (2008), 165–175) by proving that quadric plane incidence numbers imply quadric solid incidence numbers, except for the dual complete 11-cap of PG(4, 3). Furthermore, new characterizations of the parabolic quadric Q(4, q)

更新日期：2021-01-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-09

The distance distribution of a code is the vector whose ith entry is the number of pairs of codewords with distance i. We investigate the structure of the distance distribution for cyclic orbit codes, which are subspace codes generated by the action of $${\mathbb {F}}_{q^n}^*$$ on an $${\mathbb {F}}_q$$-subspace U of $${\mathbb {F}}_{q^n}$$. Note that $${\mathbb {F}}_{q^n}^*$$ is a Singer cycle in

更新日期：2021-01-10
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-09
Daniele Bartoli, Matteo Bonini, Marco Timpanella

Minimal codes are a class of linear codes which gained interest in the last years, thanks to their connections to secret sharing schemes. In this paper we provide the weight distributions and the parameters of families of minimal codes recently introduced by C. Tang, Y. Qiu, Q. Liao, Z. Zhou, answering some open questions.

更新日期：2021-01-10
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-06
Claude Carlet, Kwang Ho Kim, Sihem Mesnager

Using recent results on solving the equation $$X^{2^k+1}+X+a=0$$ over a finite field $${{\mathbb {F}}}_{2^n}$$ provided by the second and the third authors, we address an open question raised by the first author in WAIFI 2014 concerning the APN-ness of the Kasami functions $$x\mapsto x^{2^{2k}-2^k+1}$$ with $$\gcd (k,n)=1$$, $$x\in {{\mathbb {F}}}_{2^n}$$.

更新日期：2021-01-06
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2021-01-02
Chun Guo, Guoyan Zhang

Initiated by Luby and Rackoff (SIAM J. Computing, ’88), the information theoretic security of Feistel networks built upon random functions has been extensively studied. In sharp contrast, the exact security of Feistel networks built upon invertible random permutations remains largely unknown, particularly in the regime of beyond-birthday-bound. To bridge this gap, we reduce the problem to counting

更新日期：2021-01-02
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-12-19
Trygve Johnsen, Hugues Verdure

We introduce greedy weights of matroids, inspired by those for linear codes. We show that a Wei duality holds for two of these types of greedy weights for matroids. Moreover we show that in the cases where the matroids involved are associated to linear codes, our definitions coincide with those for codes. Thus our Wei duality is a generalization of that for linear codes given by Schaathun. In the last

更新日期：2020-12-20
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-12-13
Julian Renner, Alessandro Neri, Sven Puchinger

Low-rank parity-check (LRPC) codes are rank-metric codes over finite fields, which have been proposed by Gaborit et al. (Proceedings of the workshop on coding and cryptography WCC, vol 2013, 2013) for cryptographic applications. Inspired by a recent adaption of Gabidulin codes to certain finite rings by Kamche et al. (IEEE Trans Inf Theory 65(12):7718–7735, 2019), we define and study LRPC codes over

更新日期：2020-12-14
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-25
Eiichi Bannai, Manabu Oura, Da Zhao

Nebe, Rains and Sloane studied the polynomial invariants for real and complex Clifford groups and they give a new conceptual proof that these invariants are spanned by the set of complete weight enumerators of certain self-dual codes, which was first proved by Runge using modular forms. The purpose of this paper is to show that very similar results can be obtained for the invariants of the complex

更新日期：2020-11-25
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-23
Cícero Carvalho, Victor G. L. Neumann

Projective Reed-Muller codes are obtained by evaluating homogeneous polynomials of degree d in $${\mathbb {F}}_q[X_0, \ldots , X_n]$$ on the points of a projective space of dimension n defined over a finite field $${\mathbb {F}}_q$$. They were introduced by Lachaud, in 1986, and their minimum distance was determined by Serre and Sørensen. As for the higher Hamming weights, contributions were made by

更新日期：2020-11-23
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-23
Chen-Dong Ye, Tian Tian, Fan-Yang Zeng

Conditional differential attacks were proposed by Knellwolf et al. at ASIACRYPT 2010 which targeted at cryptographic primitives based on non-linear feedback shift registers. The main idea of conditional differential attacks lies in controlling the propagation of a difference through imposing some conditions on public/key variables. In this paper, we improve the conditional differential attack by introducing

更新日期：2020-11-23
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-19
Delio Jaramillo, Maria Vaz Pinto, Rafael H. Villarreal

The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed–Muller-type codes, and we determine the minimum distance of toric codes over hypersimplices, and the 1st and 2nd generalized Hamming weights of squarefree evaluation codes

更新日期：2020-11-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-10
Xiaopeng Zhao, Zhenfu Cao, Xiaolei Dong, Jun Shao

At PKC 2019, Clear and McGoldrick presented the first identity-based encryption (IBE) scheme that is group homomorphic for addition modulo a poly-sized prime e. Assuming that deciding solvability of a special system of multivariate polynomial equations is hard, they proved that their scheme for $$e>2$$ is anonymous. In this paper, we review the classical Galbraith’s test on the anonymity of the first

更新日期：2020-11-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-10
Jingkun Zhou, Zhiwen He, Zhao Chai

In this paper, we construct directed strongly regular graphs with new parameters by using partial sum families with local rings. 16 families of new directed strongly regular graphs are obtained and the uniform partial sum families are given. Based on the cyclotomic numbers of finite fields, we present two infinite families of directed strongly regular Cayley graphs from semi-direct products of groups

更新日期：2020-11-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-11-08
Sartaj Ul Hasan, Mohit Pal, Constanza Riera, Pantelimon  Stănică

We give some classes of power maps with low c-differential uniformity over finite fields of odd characteristic, for $$c=-1$$. Moreover, we give a necessary and sufficient condition for a linearized polynomial to be a perfect c-nonlinear function and investigate conditions when perturbations of perfect c-nonlinear (or not) function via an arbitrary Boolean or p-ary function is perfect c-nonlinear. In

更新日期：2020-11-09
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-31
Edoardo Ballico, Giuseppe Favacchio, Elena Guardo, Lorenzo Milazzo

The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System S(t, n, v) we associate two ideals, in a suitable polynomial ring, defining a Steiner configuration of points and its Complement. We focus on the latter, studying its homological invariants, such as Hilbert Function and Betti numbers. We also study

更新日期：2020-11-02
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-29
Alexey Oblaukhov

In this work we study metric properties of the well-known family of binary Reed–Muller codes. Let A be an arbitrary subset of the Boolean cube, and $${\widehat{A}}$$ be the metric complement of A—the set of all vectors of the Boolean cube at the maximal possible distance from A. If the metric complement of $${\widehat{A}}$$ coincides with A, then the set A is called a metrically regular set. The problem

更新日期：2020-10-30
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-28
Michael Bamiloshin, Aner Ben-Efraim, Oriol Farràs, Carles Padró

Linear information and rank inequalities as, for instance, Ingleton inequality, are useful tools in information theory and matroid theory. Even though many such inequalities have been found, it seems that most of them remain undiscovered. Improved results have been obtained in recent works by using the properties from which they are derived instead of the inequalities themselves. We apply here this

更新日期：2020-10-30
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-19
Pranab Chakraborty, Subhamoy Maitra

In this paper we provide a theoretical argument towards an unsolved question related to Mantin’s “Digraph Repetition Bias” (Eurocrypt 2005) that is observed in the key-stream of RC4. The open question, that depends on the observation that arrival of four consecutive same bytes (of the form AAAA) in RC4 key-stream is slightly negatively biased, was posed by Bricout et al (Des. Codes Cryptogr. 86:743–770

更新日期：2020-10-19
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-16
Matthias Grezet, Camilla Hollanti

This paper presents a new alphabet-dependent bound for codes with hierarchical locality. Then, the complete list of possible localities is derived for a class of codes obtained by deleting specific columns from a Simplex code. This list is used to show that these codes are optimal codes with hierarchical locality.

更新日期：2020-10-17
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-15
Xin Wang

Parent-identifying set systems and separable codes are useful combinatorial structures which were introduced, respectively, for traitor tracing in broadcast encryption and collusion-resistant fingerprints for copyright protection. Determining the maximum size of such structures is the main research objective. New upper bounds are presented in this paper. Specifically, for parent-identifying set systems

更新日期：2020-10-16
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-13
Wilfried Meidl, Isabel Pirsic

Bent functions from a vector space $${{\mathbb {V}}}_n$$ over $${{\mathbb {F}}}_2$$ of even dimension $$n=2m$$ into the cyclic group $${{\mathbb {Z}}}_{2^k}$$, or equivalently, relative difference sets in $${{\mathbb {V}}}_n\times {{\mathbb {Z}}}_{2^k}$$ with forbidden subgroup $${{\mathbb {Z}}}_{2^k}$$, can be obtained from spreads of $${{\mathbb {V}}}_n$$ for any $$k\le n/2$$. In this article, existence

更新日期：2020-10-13
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-08
P. Almeida, D. Napp

Let $${\mathbb {F}}[D]$$ be the polynomial ring with entries in a finite field $${\mathbb {F}}$$. Convolutional codes are submodules of $${\mathbb {F}}[D]^n$$ that can be described by left prime polynomial matrices. In the last decade there has been a great interest in convolutional codes equipped with a rank metric, called sum rank metric, due to their wide range of applications in reliable linear

更新日期：2020-10-08
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-07
Marco Calderini

Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken–Leander function on a subfield.

更新日期：2020-10-07
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-07
Lilya Budaghyan, Marco Calderini, Claude Carlet, Robert Coulter, Irene Villa

In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299–5309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for $$n=8$$ and produces fifteen new APN functions for $$n=9$$.

更新日期：2020-10-07
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-06
Sihem Mesnager, Sihong Su, Hui Zhang

Rotation symmetric Boolean functions incorporate a super-class of symmetric functions which represent an attractive corpus for computer investigation. These functions have been investigated from the viewpoints of bentness and correlation immunity and have also played a role in the study of nonlinearity. In the literature, many constructions of balanced odd-variable rotation symmetric Boolean functions

更新日期：2020-10-07
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-10-06
Lukas Kölsch

We explicitly determine the binary representation of the inverse of all Kasami exponents $$K_r=2^{2r}-2^r+1$$ modulo $$2^n-1$$ for all possible values of n and r. This includes as an important special case the APN Kasami exponents with $$\gcd (r,n)=1$$. As a corollary, we determine the algebraic degree of the inverses of the Kasami functions. In particular, we show that the inverse of an APN Kasami

更新日期：2020-10-07
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-25
Whan-Hyuk Choi, Hyun Jin Kim, Yoonjin Lee

We find a method for constructing DNA codes with single-deletion-correcting capability. We first present an explicit algorithm for the construction of the q-ary single-deletion-correcting codes (abbreviated as SDC codes) using a class of the complementary information set codes (abbreviated as CIS codes), where q is a power of a prime. We then show that the encoding/decoding scheme of the CIS codes

更新日期：2020-09-25
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-22
Juliane Capaverde, Ariane M. Masuda, Virgínia M. Rodrigues

Let $${\mathbb {F}}_{q}$$ be a finite field of odd characteristic. We study Rédei functions that induce permutations over $$\mathbb {P}^1({\mathbb {F}}_{q})$$ whose cycle decomposition contains only cycles of length 1 and j, for an integer $$j\ge 2$$. When j is 4 or a prime number, we give necessary and sufficient conditions for a Rédei permutation of this type to exist over $$\mathbb {P}^1({\mathbb 更新日期：2020-09-22 • Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-20 Minjia Shi, Li Xu, Patrick Solé Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual. Numerical examples show that the codes constructed have optimal or quasi-optimal parameters amongst formally self-dual codes. Self-duality, the trivial case of isoduality, can 更新日期：2020-09-20 • Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-15 Sudhir R. Ghorpade, Trygve Johnsen We consider the notion of a (q, m)-polymatroid, due to Shiromoto, and the more general notion of (q, m)-demi-polymatroid, and show how generalized weights can be defined for them. Further, we establish a duality for these weights analogous to Wei duality for generalized Hamming weights of linear codes. The corresponding results of Ravagnani for Delsarte rank metric codes, and Martínez-Peñas and Matsumoto 更新日期：2020-09-15 • Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-14 Petr Lisoněk We say that \((x,y,z)\in Q^3$$ is an associative triple in a quasigroup $$(Q,*)$$ if $$(x*y)*z=x*(y*z)$$. Let a(Q) denote the number of associative triples in Q. It is easy to show that $$a(Q)\ge |Q|$$, and we call the quasigroup maximally nonassociative if $$a(Q)= |Q|$$. It was conjectured that maximally nonassociative quasigroups do not exist when $$|Q|>1$$. Drápal and Lisoněk recently refuted this

更新日期：2020-09-14
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-12
Minjia Shi, Wang Xuan, Patrick Solé

Two infinite families of $$\mathbb {Z}_4$$-codes with two nonzero Lee weights are constructed by their generator matrices. Their Gray images are nonlinear with the same weight distribution as that of the two-weight binary codes of type SU1 in the sense of (Calderbank, Kantor, 1986).

更新日期：2020-09-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-12
Junling Zhou, Wenling Zhou

Various kinds of fingerprinting codes and their related combinatorial structures are extensively studied for protecting copyrighted materials. This paper concentrates on one specialised fingerprinting code named wide-sense frameproof codes in order to prevent innocent users from being framed. Let Q be a finite alphabet of size q. Given a t-subset $$X=\{ x ^1,\ldots , x ^t \}\subseteq Q^n$$, a position

更新日期：2020-09-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-11
Jong Yoon Hyun, Hyun Kwang Kim, Yansheng Wu, Qin Yue

Recently, some infinite families of minimal and optimal binary linear codes were constructed from simplicial complexes by Hyun et al. We extend this construction method to arbitrary posets. Especially, anti-chains are corresponded to simplicial complexes. In this paper, we present two constructions of binary linear codes from hierarchical posets of two levels. In particular, we determine the weight

更新日期：2020-09-12
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-03
Xinmei Huang, Qin Yue, Yansheng Wu, Xiaoping Shi, Jerod Michel

Linear complementary dual (LCD) codes have attracted much attention in recent years due to their applications in implementations against side-channel attacks and fault injection attacks. Comparing coset leaders, we introduce the new concept of absolute coset leaders, which provides advantages for constructing LCD BCH codes. We then give explicit presentations for the largest, second largest and third

更新日期：2020-09-03
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-02
Xinxin Gong, Bin Zhang

In this paper, we study the linear approximation of certain composition functions, with applications to SNOW 2.0 and SNOW 3G. We first propose an efficient algorithm to compute the linear approximation of certain composition functions with parallel operations, which has a linear-time complexity for any given mask tuple, and thus allows for a wide range of search for linear approximations. Naturally

更新日期：2020-09-03
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-09-02
Youngkyung Lee, Dong Hoon Lee, Jong Hwan Park

The security of public-key encryption (PKE) schemes in a multi-user setting is aimed at capturing real-world scenarios in which an adversary could attack multiple users and multiple ciphertexts of its choice. However, the fact that a real-world adversary can also mount key-exposure attacks for a set of multiple public keys requires us to consider a more realistic notion of security in multi-user settings

更新日期：2020-09-03
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-29
Cem Güneri, Edgar Martínez-Moro, Selcen Sayıcı

Linear complementary dual (LCD) codes and linear complementary pair (LCP) of codes over finite fields have been intensively studied recently due to their applications in cryptography, in the context of side channel and fault injection attacks. The security parameter for an LCP of codes (C, D) is defined as the minimum of the minimum distances d(C) and $$d(D^\bot )$$. It has been recently shown that

更新日期：2020-08-29
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-20
Delphine Boucher

After giving a new interpretation of the skew metric defined in [8], we show that the decoding algorithm of [4] for skew Reed–Solomon codes in the Hamming metric remains valid with respect to the skew metric. This enables us to make a first step towards a list decoding algorithm in the skew metric.

更新日期：2020-08-20
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-18
Khodakhast Bibak

In this paper, we make a novel connection between information theory and additive combinatorics; more specifically, between deletion/insertion correcting codes and the celebrated Littlewood–Offord problem. We see how results from one area can have an impact on the other area and vice versa. In particular, a result on the Littlewood–Offord problem gives a nice upper bound for the size of the Levenshtein

更新日期：2020-08-18
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-17
Juanjuan Xu, Jingjun Bao, Lijun Ji

A t-$$(v,k,\lambda )$$ design is a pair $$(X,\mathcal{B})$$, where X is a v-element set and $$\mathcal{B}$$ is a set of k-subsets of X, called blocks, with the property that every t-subset of X is contained in exactly $$\lambda$$ blocks. A t-$$(v,k,\lambda )$$ design $$(X,\mathcal{B})$$ is said to be $$(s,\mu )$$-resolvable if $$\mathcal{B}$$ can be partitioned into $$\mathcal{B}_1|\cdots |\mathcal{B}_c$$

更新日期：2020-08-17
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-14
Yeow Meng Chee, Charles J. Colbourn, Hoang Dau, Ryan Gabrys, Alan C. H. Ling, Dylan Lusi, Olgica Milenkovic

Storage architectures ranging from minimum bandwidth regenerating encoded distributed storage systems to declustered-parity RAIDs can employ dense partial Steiner systems to support fast reads, writes, and recovery of failed storage units. To enhance performance, popularities of the data items should be taken into account to make frequencies of accesses to storage units as uniform as possible. A combinatorial

更新日期：2020-08-14
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-14
Shizhu Tian, Christina Boura, Léo Perrin

In order to study the resistance of a block cipher against boomerang attacks, a tool called the Boomerang Connectivity Table (BCT) for S-boxes was recently introduced. Very little is known today about the properties of this table especially for bijective S-boxes defined for n variables with $$n\equiv 0 \mod 4$$. In this work we study the boomerang uniformity of some popular constructions used for building

更新日期：2020-08-14
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-07
Seyed Hassan Alavi, Ashraf Daneshkhah, Cheryl E. Praeger

In this paper, we first study biplanes $$\mathcal {D}$$ with parameters (v, k, 2), where the block size $$k\in \{13,16\}$$. These are the smallest parameter values for which a classification is not available. We show that if $$k=13$$, then either $$\mathcal {D}$$ is the Aschbacher biplane or its dual, or $$\mathbf {Aut}(\mathcal {D})$$ is a subgroup of the cyclic group of order 3. In the case where

更新日期：2020-08-08
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-08-06
Martin Ekerå

We revisit the quantum algorithm for computing short discrete logarithms that was recently introduced by Ekerå and Håstad. By carefully analyzing the probability distribution induced by the algorithm, we show its success probability to be higher than previously reported. Inspired by our improved understanding of the distribution, we propose an improved post-processing algorithm that is considerably

更新日期：2020-08-06
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-31
Yan Zhu, Naoki Watamura

Relative t-designs are defined in both P- and Q-polynomial association schemes. In this paper, we investigate relative t-designs in Johnson association schemes J(v, k) for P-polynomial structure. It is known that each nontrivial shell of J(v, k) is identified with the product of two smaller Johnson association schemes. We prove that relative t-designs in J(v, k) supported by one shell are equivalent

更新日期：2020-08-01
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-03
Ignacio García-Marco, Irene Márquez-Corbella, Diego Ruano

Given a linear code $${\mathcal {C}}$$, its square code $${\mathcal {C}}^{(2)}$$ is the span of all component-wise products of two elements of $${\mathcal {C}}$$. Motivated by applications in multi-party computation, our purpose with this work is to answer the following question: which families of affine variety codes have simultaneously high dimension $$k({\mathcal {C}})$$ and high minimum distance

更新日期：2020-07-24
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-08
Alain Couvreur, Isabella Panaccione

We present a new decoding algorithm based on error locating pairs and correcting an amount of errors exceeding half the minimum distance. When applied to Reed–Solomon or algebraic geometry codes, the algorithm is a reformulation of the so-called power decoding algorithm. Asymptotically, it corrects errors up to Sudan’s radius. In addition, this new framework applies to any code benefiting from an error

更新日期：2020-07-24
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-06-21
Umberto Martínez-Peñas

Sum-rank Hamming codes are introduced in this work. They are essentially defined as the longest codes (thus of highest information rate) with minimum sum-rank distance at least 3 (thus one-error-correcting) for a fixed redundancy r, base-field size q and field-extension degree m (i.e., number of matrix rows). General upper bounds on their code length, number of shots or sublengths and average sublength

更新日期：2020-07-24
• Des. Codes Cryptogr. (IF 1.224) Pub Date : 2020-07-24
Yunwen Liu, Wenying Zhang, Bing Sun, Vincent Rijmen, Guoqiang Liu, Chao Li, Shaojing Fu, Meichun Cao

For differential cryptanalysis under the single-key model, the key schedules hardly need to be exploited in constructing the characteristics, which is based on the hypothesis of stochastic equivalence. In this paper, we study a profound effect of the key schedules on the validity of the differential characteristics. Noticing the sensitivity in the probability of the characteristics to specific keys

更新日期：2020-07-24
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