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Lifting iso-dual algebraic geometry codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-05-07 María Chara, Ricardo Podestá, Luciane Quoos, Ricardo Toledano
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Yoyo attack on 4-round Lai-Massey scheme with secret round functions Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-05-03 Le Dong, Danxun Zhang, Wenya Li, Wenling Wu
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Characterization of weakly regular p-ary bent functions of $$\ell $$ -form Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-05-02 Jong Yoon Hyun, Jungyun Lee, Yoonjin Lee
We study the essential properties of weakly regular p-ary bent functions of \(\ell \)-form, where a p-ary function is from \(\mathbb {F}_{p^m}\) to \(\mathbb {F}_p\). We observe that most of studies on a weakly regular p-ary bent function f with \(f(0)=0\) of \(\ell \)-form always assume the gcd-condition: \(\gcd (\ell -1,p-1)=1\). We first show that whenever considering weakly regular p-ary bent functions
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Computing gluing and splitting $$(\ell ,\ell )$$ -isogenies Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-05-02 Song Tian
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Optimal $$(r,\delta )$$ -LRCs from monomial-Cartesian codes and their subfield-subcodes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-05-02 C. Galindo, F. Hernando, H. Martín-Cruz
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On the packing density of Lee spheres Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-30 Ang Xiao, Yue Zhou
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Special directions on the finite affine plane Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-29 Gergely Kiss, Gábor Somlai
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Subgroup total perfect codes in Cayley sum graphs Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-29 Xiaomeng Wang, Lina Wei, Shou-Jun Xu, Sanming Zhou
Let \(\Gamma \) be a graph with vertex set V, and let a, b be nonnegative integers. An (a, b)-regular set in \(\Gamma \) is a nonempty proper subset D of V such that every vertex in D has exactly a neighbours in D and every vertex in \(V \setminus D\) has exactly b neighbours in D. In particular, a (1, 1)-regular set is called a total perfect code. Let G be a finite group and S a square-free subset
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Small weight codewords of projective geometric codes II Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-28 Sam Adriaensen, Lins Denaux
The \(p\)-ary linear code \(\mathcal {C}_{k}\!\left( n,q\right) \) is defined as the row space of the incidence matrix \(A\) of \(k\)-spaces and points of \(\textrm{PG}\!\left( n,q\right) \). It is known that if \(q\) is square, a codeword of weight \(q^k\sqrt{q}+\mathcal {O}\!\left( q^{k-1}\right) \) exists that cannot be written as a linear combination of at most \(\sqrt{q}\) rows of \(A\). Over
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Further results on covering codes with radius R and codimension $$tR+1$$ Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-27 Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco
The length function \(\ell _q(r,R)\) is the smallest possible length n of a q-ary linear \([n,n-r]_qR\) code with codimension (redundancy) r and covering radius R. Let \(s_q(N,\rho )\) be the smallest size of a \(\rho \)-saturating set in the projective space \(\textrm{PG}(N,q)\). There is a one-to-one correspondence between \([n,n-r]_qR\) codes and \((R-1)\)-saturating n-sets in \(\textrm{PG}(r-1
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Using $$P_\tau $$ property for designing bent functions provably outside the completed Maiorana–McFarland class Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-22 Enes Pasalic, Amar Bapić, Fengrong Zhang, Yongzhuang Wei
In this article, we identify certain instances of bent functions, constructed using the so-called \(P_\tau \) property, that are provably outside the completed Maiorana–McFarland (\({\mathcal{M}\mathcal{M}}^\#\)) class. This also partially answers an open problem in posed by Kan et al. (IEEE Trans Inf Theory, https://doi.org/10.1109/TIT.2022.3140180, 2022). We show that this design framework (using
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Chain-imprimitive, flag-transitive 2-designs Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-20 Carmen Amarra, Alice Devillers, Cheryl E. Praeger
We consider 2-designs which admit a group of automorphisms that is flag-transitive and leaves invariant a chain of nontrivial point-partitions. We build on our recent work on 2-designs which are block-transitive but not necessarily flag-transitive. In particular we use the concept of the “array” of a point subset with respect to the chain of point-partitions; the array describes the distribution of
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Meet-in-the-middle attacks on AES with value constraints Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-18 Xiaoli Dong, Jun Liu, Yongzhuang Wei, Wen Gao, Jie Chen
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Symmetric 2-adic complexity of Tang–Gong interleaved sequences from generalized GMW sequence pair Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Bo Yang, Kangkang He, Xiangyong Zeng, Zibi Xiao
Tang–Gong interleaved sequences constructed from the generalized GMW sequence pair are a class of binary sequences with optimal autocorrelation magnitude. In this paper, the symmetric 2-adic complexity of these sequences is investigated. We first derive a lower bound on their 2-adic complexity by extending the method proposed by Hu. Then, by analysing the algebraic structure of these sequences, a lower
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Constructing linked systems of relative difference sets via Schur rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Mikhail Muzychuk, Grigory Ryabov
In the present paper, we study relative difference sets (RDSs) and linked systems of them. It is shown that a closed linked system of RDSs is always graded by a group. Based on this result, we also define a product of RDS linked systems sharing the same grading group. Further, we generalize the Davis-Polhill-Smith construction of a linked system of RDSs. Finally, we construct new linked system of RDSs
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Fast decoding of lifted interleaved linearized Reed–Solomon codes for multishot network coding Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-16 Hannes Bartz, Sven Puchinger
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Lengths of divisible codes: the missing cases Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-13 Sascha Kurz
A linear code C over \({\mathbb {F}}_q\) is called \(\Delta \)-divisible if the Hamming weights \({\text {wt}}(c)\) of all codewords \(c \in C\) are divisible by \(\Delta \). The possible effective lengths of \(q^r\)-divisible codes have been completely characterized for each prime power q and each non-negative integer r in Kiermaier and Kurz (IEEE Trans Inf Theory 66(7):4051–4060, 2020). The study
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New constructions of signed difference sets Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-10 Zhiwen He, Tingting Chen, Gennian Ge
Signed difference sets have interesting applications in communications and coding theory. A \((v,k,\lambda )\)-difference set in a finite group G of order v is a subset D of G with k distinct elements such that the expressions \(xy^{-1}\) for all distinct two elements \(x,y\in D\), represent each non-identity element in G exactly \(\lambda \) times. A \((v,k,\lambda )\)-signed difference set is a generalization
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Algebraic properties of the maps $$\chi _n$$ Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-10 Jan Schoone, Joan Daemen
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Jacobi polynomials for the first-order generalized Reed–Muller codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-08 Ryosuke Yamaguchi
In this paper, we give the Jacobi polynomials for first-order generalized Reed–Muller codes. We show as a corollary the nonexistence of combinatorial 3-designs in these codes.
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Anonymous attribute-based broadcast encryption with hidden multiple access structures Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-06 Tran Viet Xuan Phuong
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Ovoids of Q(6, q) of low degree Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-06 Daniele Bartoli, Nicola Durante, Giovanni Giuseppe Grimaldi
Ovoids of the parabolic quadric Q(6, q) of \(\textrm{PG}(6,q)\) have been largely studied in the last 40 years. They can only occur if q is an odd prime power and there are two known families of ovoids of Q(6, q), the Thas-Kantor ovoids and the Ree-Tits ovoids, both for q a power of 3. It is well known that to any ovoid of Q(6, q) two polynomials \(f_1(X,Y,Z)\), \(f_2(X,Y,Z)\) can be associated. In
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On the size distribution of the fixed-length Levenshtein balls with radius one Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-05 Geyang Wang, Qi Wang
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Special overlarge sets of Kirkman triple systems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-05 Juanjuan Xu, Lijun Ji
A Steiner quadruple system of order \(v+1\) with resolvable derived designs (every derived Steiner triple system of order v at a point is resolvable), abbreviated as RDSQS\((v+1)\), has been used to construct a large set of Kirkman triple systems of order 3v. In this paper, an RDSQS\((v+1)\) is reduced to an overlarge set of Kirkman triple systems of order v with an additional property (OLKTS\(^+(v)\))
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Combinatorial constructions of optimal low-power error-correcting cooling codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-04 Shuangqing Liu, Lijun Ji
High temperatures have dramatic negative effects on interconnect performance. In a bus, whenever the state transitions from “0” to “1”, or “0” to “1”, joule heating causes the temperature to rise. A low-power error-correcting cooling (LPECC) code, introduced in Chee et al. (IEEE Trans Inf Theory 64:3062–3085, 2018), is a coding scheme which can be used to control the peak temperature, the average power
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Construction of quantum codes from multivariate polynomial rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-02 Cong Yu, Shixin Zhu, Fuyin Tian
In this paper, we use multivariate polynomial rings to construct quantum error-correcting codes (QECCs) via Hermitian construction. We establish a relation between linear codes and ideals of multivariate polynomial rings. We give a necessary and suffcient condition for a multivariate polynomial to generate a Hermitian dual-containing code. By comparing with the literatures in recent years, we construct
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Optimal binary signed-digit representations of integers and the Stern polynomial Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-04-02 Laura Monroe
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Preimage attacks on reduced-round Ascon-Xof Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-30 Seungjun Baek, Giyoon Kim, Jongsung Kim
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Families of quadratic sets on the Klein quadric Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-30 Bart De Bruyn
Consider the Klein quadric \(Q^+(5,q)\) in \(\text{ PG }(5,q)\). A set of points of \(Q^+(5,q)\) is called a quadratic set if it intersects each plane \(\pi \) of \(Q^+(5,q)\) in a possibly reducible conic of \(\pi \), i.e. in a singleton, a line, an irreducible conic, a pencil of two lines or the whole of \(\pi \). A quadratic set is called good if at most two of these possibilities occur as \(\pi
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Classifying pseudo-ovals, translation generalized quadrangles, and elation Laguerre planes of small order Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-29 Giusy Monzillo, Tim Penttila, Alessandro Siciliano
We provide classification results for translation generalized quadrangles of order less than or equal to 64, and hence, for all incidence geometries related to them. The results consist of the classification of all pseudo-ovals in \(\textrm{PG}(3n-1,2)\), for \(n=3,4\), and that of the pseudo-ovals in \(\textrm{PG}(3n-1,q)\), for \(n=5,6\), such that one of the associated projective planes is Desarguesian
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Classification of semiregular relative difference sets with $$\gcd (\lambda ,n)=1$$ attaining Turyn’s bound Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Ka Hin Leung, Bernhard Schmidt, Tao Zhang
Suppose a \((\lambda n,n,\lambda n, \lambda )\) relative difference set exists in an abelian group \(G=S\times H\), where \(|S|=\lambda \), \(|H|=n^2\), \(\gcd (\lambda ,n)=1\), and \(\lambda \) is self-conjugate modulo \(\lambda n\). Then \(\lambda \) is a square, say \(\lambda =u^2\), and \(\exp (S)\) divides u by Turyn’s exponent bound. We classify all such relative difference sets with \(\exp (S)=u\)
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Efficient secure multi-party computation for proof of custody in Ethereum sharding Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Yuxin Tong, Xiang Xie, Kang Yang, Rui Zhang, Rui Xue
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PERK: compact signature scheme based on a new variant of the permuted kernel problem Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-27 Slim Bettaieb, Loïc Bidoux, Victor Dyseryn, Andre Esser, Philippe Gaborit, Mukul Kulkarni, Marco Palumbi
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CCA security for contracting (quasi-)Feistel constructions with tight round complexity Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-23 Chun Guo, Ling Song
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On Bose distance of a class of BCH codes with two types of designed distances Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-19 Chunyu Gan, Chengju Li, Haifeng Qian, Xueying Shi
BCH codes are an interesting class of cyclic codes with good error-correcting capability and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Let \(\mathbb {F}_q\) be the finite field of size q and \(n=q^m-1\), where m is a positive integer. Let \(\mathcal C_{(q, m, \delta )}\) be the primitive narrow-sense BCH codes of length n over
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Negacyclic BCH codes of length $$\frac{q^{2m}-1}{q+1}$$ and their duals Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-19 Zhonghua Sun, Xinyue Liu, Shixin Zhu, Yongsheng Tang
Negacyclic BCH codes are an important subclass of negacyclic codes and have good parameters. Inspired by the recent work on cyclic codes published in Wu et al. (Finite Fields Appl 60:101581, 2019), the objective of this paper is to investigate the parameters of the narrow-sense negacyclic BCH codes of length \(n=\frac{q^{2m}-1}{q+1}\) over \({\textrm{GF}}(q)\), where q is an odd prime power. For \(2\le
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Balanced reconstruction codes for single edits Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-16 Rongsheng Wu, Xiande Zhang
Motivated by the sequence reconstruction problem initiated by Levenshtein, reconstruction codes were introduced by Cai et al. to combat errors when a fixed number of noisy channels are available. The central problem on this topic is to design codes with sizes as large as possible, such that every codeword can be uniquely reconstructed from any N distinct noisy reads, where N is fixed. In this paper
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Impossibility of efficient information-theoretic fuzzy extraction Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-14 Benjamin Fuller
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Monomial isomorphism for tensors and applications to code equivalence problems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12 Giuseppe D’Alconzo
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Efficient computation of $$(2^n,2^n)$$ -isogenies Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12 S. Kunzweiler
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Square root computation in finite fields Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-12 Ebru Adiguzel-Goktas, Enver Ozdemir
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Some constructions and existence conditions for Hermitian self-dual skew codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-10 Delphine Boucher, Kayodé Epiphane Nouetowa
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MDS codes with l-Galois hulls of arbitrary dimensions Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-09 Liqin Qian, Xiwang Cao, Xia Wu, Wei Lu
The hull of a linear code is defined to be the intersection of the code and its dual, and was originally introduced to classify finite projective planes. The objective of this paper is to construct some MDS codes with l-Galois hulls of arbitrary dimensions by using the generalized Reed–Solomon codes over finite fields with regard to l-Galois inner product. We give a general construction theorem and
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Compressed M-SIDH: an instance of compressed SIDH-like schemes with isogenies of highly composite degrees Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05 Kaizhan Lin, Jianming Lin, Shiping Cai, Weize Wang, Chang-An Zhao
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Extremal regular graphs and hypergraphs related to fractional repetition codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05 Hongna Yang, Yiwei Wang, Yiwei Zhang
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Linear codes associated to determinantal varieties in the space of hermitian matrices Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-05 Kanchan Singh, Ritesh Kumar Pathak, Sheo Kumar Singh
We introduce a new class of linear codes over a finite field associated to determinantal varieties in the space of hermitian matrices and determine their length, dimension and minimum distance along with the weight spectrum.
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Large Hermitian hull GRS codes of any given length Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04 Hao Chen
The construction of Hermitian self-orthogonal generalized Reed-Solomon (GRS) codes of many specific lengths and large dimensions has been an active topic. The construction of Euclidean self-dual GRS codes and twisted generalized Reed-Solomon (TGRS) codes attracts some attentions. In this paper, we construct GRS \([n, k, n-k+1]_{q^2}\) codes (thus MDS codes) over \(\textbf{F}_{q^2}\) of the arbitrary
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Twisted skew G-codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04 Angelot Behajaina, Martino Borello, Javier de la Cruz, Wolfgang Willems
In this paper we investigate left ideals as codes in twisted skew group rings. The considered rings, which are in most cases algebras over a finite field, allow us to retrieve many of the well-known codes. The presentation, given here, unifies the concept of group codes, twisted group codes and skew group codes.
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Combining MILP modeling with algebraic bias evaluation for linear mask search: improved fast correlation attacks on SNOW Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-04 Xinxin Gong, Yonglin Hao, Qingju Wang
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A conceptually simple and generic construction of plaintext checkable encryption in the standard model Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-24
Abstract Plaintext-checkable encryption (PCE) can support searches over ciphertext by directly using plaintext. The functionality of a search is modeled by a specific check algorithm that takes a pair of target plaintext and ciphertext as input and returns 1 if the correct decryption result of the ciphertext is identical to the target plaintext. A trivial solution is to use an existing scheme (e.g
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Leakage-resilient $$\textsf {IBE} $$ / $$\textsf {ABE} $$ with optimal leakage rates from lattices Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-24 Qiqi Lai, Feng-Hao Liu, Zhedong Wang
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Self-dual codes from a block matrix construction characterised by group rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-22 Adam Michael Roberts
We give a new technique for constructing self-dual codes based on a block matrix whose blocks arise from group rings and orthogonal matrices. The technique can be used to construct self-dual codes over finite commutative Frobenius rings of characteristic 2. We give and prove the necessary conditions needed for the technique to produce self-dual codes. We also establish the connection between self-dual
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On the sequential indifferentiability of the Lai–Massey construction Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-17 Chun Guo, Yiyuan Luo, Chenyu Xiao
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Using alternating de Bruijn sequences to construct de Bruijn tori Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-06
Abstract A de Bruijn torus is the two dimensional generalization of a de Bruijn sequence. While methods exist to generate these tori, only a few methods of construction are known. We present a novel method to generate de Bruijn tori with rectangular windows by combining two variants of de Bruijn sequences.
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A recursive construction of doubly resolvable Steiner quadruple systems Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Zhaoping Meng, Qingling Gao, Zhanggui Wu
Two resolutions of the same 3-design are said to be orthogonal when each parallel class of one resolution has at most one block in common with each parallel class of the other resolution. If a Steiner quadruple system has two mutually orthogonal resolutions, the design is called doubly resolvable and denoted by DRSQS. In this paper, we define almost doubly resolvable candelabra quadruple system and
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On the parameters of extended primitive cyclic codes and the related designs Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Haode Yan, Yanan Yin
Very recently, Heng et al. studied a family of extended primitive cyclic codes. It was shown that the supports of all codewords with any fixed nonzero Hamming weight in this code support a 2-design. In this paper, we study this family of extended primitive cyclic codes in more details. The weight distribution is determined and the parameters of the related 2-designs are also given. Moreover, we prove
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Perfect mixed codes from generalized Reed–Muller codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-02-05 Alexander M. Romanov
In this paper, we propose a new method for constructing 1-perfect mixed codes in the Cartesian product \(\mathbb {F}_{n} \times \mathbb {F}_{q}^n\), where \(\mathbb {F}_{n}\) and \(\mathbb {F}_{q}\) are finite fields of orders \(n = q^m\) and q. We consider generalized Reed-Muller codes of length \(n = q^m\) and order \((q - 1)m - 2\). Codes whose parameters are the same as the parameters of generalized
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Infinite families of minimal binary codes via Krawtchouk polynomials Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-22 Xiaoni Du, René Rodríguez, Hao Wu
Linear codes play a crucial role in various fields of engineering and mathematics, including data storage, communication, cryptography, and combinatorics. Minimal linear codes, a subset of linear codes, are particularly essential for designing effective secret sharing schemes. In this paper, we introduce several classes of minimal binary linear codes by carefully selecting appropriate Boolean functions
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Predicate encryption with selective-opening security for receivers: formal definition, generic construction, and concrete instantiations for several primitives Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-20 Yi-Fan Tseng, Zi-Yuan Liu, Raylin Tso
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Sperner’s theorem for non-free modules over finite chain rings Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-20 Ivan Landjev, Emiliyan Rogachev
We prove Sperner-type theorems for the partially ordered set \(\mathcal {P}_M\) of all submodules of a non-free finitely generated module \({}_RM\) over a finite chain ring R. We demonstrate that the partially ordered set \(\mathcal {P}_M\) is not necessarily of Sperner type and solve the problem for modules of shape \(2^11^n\). This result is further generalized for modules of shape \(m^11^n\) over