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Non-linear MRD codes from cones over exterior sets Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-18 Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi
By using the notion of a d-embedding \(\Gamma \) of a (canonical) subgeometry \(\Sigma \) and of exterior sets with respect to the h-secant variety \(\Omega _{h}({\mathcal {A}})\) of a subset \({\mathcal {A}}\), \( 0 \le h \le n-1\), in the finite projective space \({\textrm{PG}}(n-1,q^n)\), \(n \ge 3\), in this article we construct a class of non-linear (n, n, q; d)-MRD codes for any \( 2 \le d \le
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Arithmetization-oriented APN permutations Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-18 Lilya Budaghyan, Mohit Pal
Recently, many cryptographic primitives such as homomorphic encryption (HE), multi-party computation (MPC) and zero-knowledge (ZK) protocols have been proposed in the literature which operate on the prime field \({\mathbb {F}}_p\) for some large prime p. Primitives that are designed using such operations are called arithmetization-oriented primitives. As the concept of arithmetization-oriented primitives
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Capacity of an infinite family of networks related to the diamond network for fixed alphabet sizes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-17 Sascha Kurz
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Designs in finite classical polar spaces Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-17 Michael Kiermaier, Kai-Uwe Schmidt, Alfred Wassermann
Combinatorial designs have been studied for nearly 200 years. 50 years ago, Cameron, Delsarte, and Ray-Chaudhury started investigating their q-analogs, also known as subspace designs or designs over finite fields. Designs can be defined analogously in finite classical polar spaces, too. The definition includes the m-regular systems from projective geometry as the special case where the blocks are generators
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A common generalization of hypercube partitions and ovoids in polar spaces Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-17 Jozefien D’haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt
We investigate what we call generalized ovoids, that is families of totally isotropic subspaces of finite classical polar spaces such that each maximal totally isotropic subspace contains precisely one member of that family. This is a generalization of ovoids in polar spaces as well as the natural q-analog of a subcube partition of the hypercube (which can be seen as a polar space with \(q=1\)). Our
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On the uniqueness of balanced complex orthogonal design Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-03 Yiwen Gao, Yuan Li, Haibin Kan
Complex orthogonal designs (CODs) have been used to construct space-time block codes. Its real analog, real orthogonal designs, or equivalently, sum of squares composition formula, have a long history in mathematics. Driven by some practical considerations, Adams et al. (IEEE Trans Info Theory, 57(4):2254–2262, 2011) introduced the definition of balanced complex orthogonal designs (BCODs). The code
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Minimal abundant packings and choosability with separation Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-03 Zoltán Füredi, Alexandr Kostochka, Mohit Kumbhat
A (v, k, t) packing of size b is a system of b subsets (blocks) of a v-element underlying set such that each block has k elements and every t-set is contained in at most one block. P(v, k, t) stands for the maximum possible b. A packing is called abundant if \(b> v\). We give new estimates for P(v, k, t) around the critical range, slightly improving the Johnson bound and asymptotically determine the
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Time-based attribute-based proxy re-encryption with decryption key update Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-31 Feixiang Zhao, Jian Weng, Wenli Xie, Lin Hou, Ming Li
Proxy re-encryption (PRE) is a cryptosystem that realizes efficient encrypted data sharing by allowing a third party proxy to transform a ciphertext intended for a delegator (i.e., Alice) to a ciphertext intended for a delegatee (i.e., Bob). Attribute-based proxy re-encrypftion (AB-PRE) generalizes PRE to the attribute-based scenarios, enabling fine-grained access control on ciphertexts. However, the
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Moments of autocorrelation demerit factors of binary sequences Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-01 Daniel J. Katz, Miriam E. Ramirez
Sequences with low aperiodic autocorrelation are used in communications and remote sensing for synchronization and ranging. The autocorrelation demerit factor of a sequence is the sum of the squared magnitudes of its autocorrelation values at every nonzero shift when we normalize the sequence to have unit Euclidean length. The merit factor, introduced by Golay, is the reciprocal of the demerit factor
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Bandersnatch: a fast elliptic curve built over the BLS12-381 scalar field Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-01 Simon Masson, Antonio Sanso, Zhenfei Zhang
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Storage codes and recoverable systems on lines and grids Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-09-01 Alexander Barg, Ohad Elishco, Ryan Gabrys, Geyang Wang, Eitan Yaakobi
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Frequency distance sequences for packet detection in physical-layer security Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-31 Radi Abubaker, Guang Gong
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On the construction of certain odd degree irreducible polynomials over finite fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-27 Melek Çil, Barış Bülent Kırlar
For an odd prime power q, let \(\mathbb {F}_{q^2}=\mathbb {F}_q(\alpha )\), \(\alpha ^2=t\in \mathbb {F}_q\) be the quadratic extension of the finite field \(\mathbb {F}_q\). In this paper, we consider the irreducible polynomials \(F(x)=x^k-c_1x^{k-1}+c_2x^{k-2}-\cdots -c_{2}^qx^2+c_{1}^qx-1\) over \(\mathbb {F}_{q^2}\), where k is an odd integer and the coefficients \(c_i\) are in the form \(c_i=a_i+b_i\alpha
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An algebraic approach to circulant column parity mixers Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-21 Robert Christian Subroto
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On Boolean functions derived from linear maps over $$\mathbb {Z}_4$$ and their application to secret sharing Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-16 Deepak Agrawal, Srinivasan Krishnaswamy, Smarajit Das
The Gray map converts a symbol in \(\mathbb {Z}_4\) to a pair of binary symbols. Therefore, under the Gray map, a linear function from \(\mathbb {Z}_4^n\) to \(\mathbb {Z}_4\) gives rise to a pair of boolean functions from \(\mathbb {F}_2^{2n}\) to \(\mathbb {F}_2\). This paper studies such boolean functions. We state and prove a condition for the nonlinearity of such functions and derive closed-form
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On the maximum size of ultrametric orthogonal sets over discrete valued fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-16 Noy Soffer Aranov, Angelot Behajaina
Let \({\mathcal {K}}\) be a discrete valued field with finite residue field. In analogy with orthogonality in the Euclidean space \({\mathbb {R}}^n\), there is a well-studied notion of “ultrametric orthogonality” in \({\mathcal {K}}^n\). In this paper, motivated by a question of Erdős in the real case, given integers \(k \ge \ell \ge 2\), we investigate the maximum size of a subset \(S \subseteq {\mathcal
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New distance bounds for quasi-cyclic codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-14 Ferruh Özbudak, Buket Özkaya
We consider the minimum weight of codewords in a quasi-cyclic code and characterize the estimate in its most general setup using their concatenated structure. The new bound we derive generalizes the Jensen and Güneri–Özbudak bounds and it holds for the more general class of multilevel concatenated codes.
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Involutions of finite abelian groups with explicit constructions on finite fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-12 Ruikai Chen, Sihem Mesnager
In this paper, we study properties and constructions of a general family of involutions of finite abelian groups, especially those of finite fields. The involutions we are interested in have the form \(\lambda +g\circ \tau \), where \(\lambda \) and \(\tau \) are endomorphisms of a finite abelian group and g is an arbitrary map on this group. We present some involutions explicitly written as polynomials
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Optimal $$(2,\delta )$$ locally repairable codes via punctured simplex codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-12 Yuan Gao, Weijun Fang, Jingke Xu, Dong Wang, Sihuang Hu
Locally repairable codes (LRCs) have attracted a lot of attention due to their applications in distributed storage systems. In this paper, we provide new constructions of optimal \((2, \delta )\)-LRCs over \(\mathbb {F}_q\) with flexible parameters. Firstly, employing techniques from finite geometry, we introduce a simple yet useful condition to ensure that a punctured simplex code becomes a \((2,
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Functional commitments for arbitrary circuits of bounded sizes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-12 Jinrui Sha, Shengli Liu, Shuai Han
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An algebraic algorithm for breaking NTRU with multiple keys Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-10 Shi Bai, Hansraj Jangir, Tran Ngo, William Youmans
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Reduction for block-transitive t- $$(k^2,k,\lambda )$$ designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-09 Haiyan Guan, Shenglin Zhou
In this paper, we study block-transitive automorphism groups of t-\((k^2,k,\lambda )\) designs. We prove that a block-transitive automorphism group G of a t-\((k^2,k,\lambda )\) design must be point-primitive, and G is either an affine group or an almost simple group. Moreover, the nontrivial t-\((k^2,k,\lambda )\) designs admitting block-transitive automorphism groups of almost simple type with sporadic
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Towards a classification of permutation binomials of the form $$x^i+ax$$ over $${\mathbb {F}}_{2^n}$$ Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-09 Yi Li, Xiutao Feng, Qiang Wang
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Nontrivial t-designs in polar spaces exist for all t Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-07 Charlene Weiß
A finite classical polar space of rank n consists of the totally isotropic subspaces of a finite vector space over \(\mathbb {F}_q\) equipped with a nondegenerate form such that n is the maximal dimension of such a subspace. A t-\((n,k,\lambda )\) design in a finite classical polar space of rank n is a collection Y of totally isotropic k-spaces such that each totally isotropic t-space is contained
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Cryptanalysis of a key exchange protocol based on a modified tropical structure Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-08-03 Huawei Huang, Changgen Peng, Lunzhi Deng
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The classifications of o-monomials and of 2-to-1 binomials are equivalent Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-30 Lukas Kölsch, Gohar Kyureghyan
We observe that on the binary finite fields the classification of 2-to-1 binomials is equivalent to the classification of o-monomials, which is a well-studied and elusive problem in finite geometry. This connection implies a complete classification of 2-to-1 binomials \(b=x^d+ux^e\) for a large set of values of (d, e). Further, we show that a number of the known infinite families of 2-to-1 maps can
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$$\textsf {TOPAS}$$ 2-pass key exchange with full perfect forward secrecy and optimal communication complexity Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-27 Sven Schäge
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Investigation of the permutation and linear codes from the Welch APN function Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-27 Tor Helleseth, Chunlei Li, Yongbo Xia
Dobbertin in 1999 proved that the Welch power function \(x^{2^m+3}\) was almost perferct nonlinear (APN) over the finite field \(\mathbb {F}_{2^{2m+1}}\), where m is a positive integer. In his proof, Dobbertin showed that the APNness of \(x^{2^m+3}\) essentially relied on the bijectivity of the polynomial \(g(x)=x^{2^{m+1}+1}+x^3+x\) over \(\mathbb {F}_{2^{2m+1}}\). In this paper, we first determine
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Compact FE for unbounded attribute-weighted sums for logspace from SXDH Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-27 Pratish Datta, Tapas Pal, Katsuyuki Takashima
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Two new constructions of cyclic subspace codes via Sidon spaces Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-24 Shuhui Yu, Lijun Ji
A subspace of a finite field is called a Sidon space if the product of any two of its nonzero elements is unique up to a scalar multiplier from the base field. Sidon spaces, introduced by Roth et al. in (IEEE Trans Inf Theory 64(6):4412–4422, 2018), have a close connection with optimal full-length orbit codes. In this paper, we will construct several families of large cyclic subspace codes based on
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Utilizing FWT in linear cryptanalysis of block ciphers with various structures Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-25 Yin Lv, Danping Shi, Lei Hu, Yi Guo
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MDS array codes with efficient repair and small sub-packetization level Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-23 Lei Li, Xinchun Yu, Chenhao Ying, Liang Chen, Yuanyuan Dong, Yuan Luo
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Security analysis of P-SPN schemes against invariant subspace attack with inactive S-boxes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-21 Bolin Wang, Wenling Wu
The security requirements of new applications such as cloud computing, big data, and the Internet of Things have promoted the development and application of security protocols such as secure multi-party computation, fully homomorphic encryption, and zero-knowledge proof. In order to meet these demands, there is a need for new symmetric ciphers that minimize multiplications in \( {\mathbb {F}}_{2^{n}}
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eSTARK: extending STARKs with arguments Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-20 Héctor Masip-Ardevol, Jordi Baylina-Melé, Marc Guzmán-Albiol, Jose Luis Muñoz-Tapia
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New and improved formally self-dual codes with small hulls from polynomial four Toeplitz codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-20 Yang Li, Shitao Li, Shixin Zhu
Formally self-dual (FSD) codes and linear codes with small Euclidean (resp. Hermitian) hulls have recently attracted a lot of attention due to their theoretical and practical importance. However, there has been not much attention on FSD codes with small hulls. In this paper, we introduce two kinds of polynomial four Toeplitz codes and prove that they must be FSD. We characterize the linear complementary
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A class of functions and their application in constructing semisymmetric designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-20 Robert S. Coulter, Bradley Fain
We introduce the notion of a semiplanar function of index \(\lambda \), generalising several previous concepts. We show how semiplanar functions can be used to construct semisymmetric designs using an incidence structure determined by the function. Issues regarding the connectivity of the structure are then considered. The question of existence is addressed by establishing monomial examples over finite
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CSI-Otter: isogeny-based (partially) blind signatures from the class group action with a twist Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-17 Shuichi Katsumata, Yi-Fu Lai, Jason T. LeGrow, Ling Qin
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Non-canonical maximum cliques without a design structure in the block graphs of 2-designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-18 Sergey Goryainov, Elena V. Konstantinova
In this note we answer positively a question of Chris Godsil and Karen Meagher on the existence of a 2-design whose block graph has a non-canonical maximum clique without a design structure.
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Curve-lifted codes for local recovery using lines Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-17 Gretchen L. Matthews, Travis Morrison, Aidan W. Murphy
In this paper, we introduce curve-lifted codes over fields of arbitrary characteristic, inspired by Hermitian-lifted codes over \(\mathbb {F}_{2^r}\). These codes are designed for locality and availability, and their particular parameters depend on the choice of curve and its properties. Due to the construction, the numbers of rational points of intersection between curves and lines play a key role
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Hulls of cyclic codes with respect to the regular permutation inner product Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-15 Xiaoshan Quan, Qin Yue, Fuqing Sun
In this paper, we introduce regular permutation inner products which contain the Euclidean inner product. And we generalize some properties of the Euclidean inner product to regular permutation inner products. As application, we construct a lot of cyclic codes with specific regular permutation hulls and also obtain the dimensions and distances of some BCH codes.
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Explicit constructions of NMDS self-dual codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-12 Dongchun Han, Hanbin Zhang
Near maximum distance separable (NMDS) codes are important in finite geometry and coding theory. Self-dual codes are closely related to combinatorics, lattice theory, and have important application in cryptography. In this paper, we construct a class of q-ary linear codes and prove that they are either MDS or NMDS which depends on certain zero-sum condition. In the NMDS case, we provide an effective
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New spence difference sets Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-10 James A. Davis, John Polhill, Ken Smith, Eric Swartz, Jordan Webster
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Additivity of symmetric and subspace 2-designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-05 Marco Buratti, Anamari Nakić
A 2-\((v,k,\lambda )\) design is additive (or strongly additive) if it is possible to embed it in a suitable abelian group G in such a way that its block set is contained in (or coincides with) the set of all zero-sum k-subsets of its point set. Explicit results on the additivity or strong additivity of symmetric designs and subspace 2-designs are presented. In particular, the strong additivity of
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Vectorial negabent concepts: similarities, differences, and generalizations Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-05 Nurdagül Anbar, Sadmir Kudin, Wilfried Meidl, Enes Pasalic, Alexandr Polujan
In Pasalic et al. (IEEE Trans Inf Theory 69:2702–2712, 2023), and in Anbar and Meidl (Cryptogr Commun 10:235–249, 2018), two different vectorial negabent and vectorial bent-negabent concepts are introduced, which leads to seemingly contradictory results. One of the main motivations for this article is to clarify the differences and similarities between these two concepts. Moreover, the negabent concept
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Around LCD group codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-05 Javier de la Cruz, Wolfgang Willems
In this note we answer some questions on \(\text{ LCD }\) group codes posed in de la Cruz and Willems (Des Codes Cryptogr 86:2065–2073, 2018) and (Vietnam J Math 51:721–729, 2023). Furthermore, over prime fields we determine completely the p-part of the divisor of an \(\text{ LCD }\) group code. In addition we present a natural construction of nearly \(\text{ LCD }\) codes.
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Some self-dual codes and isodual codes constructed by matrix product codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-04 Xu Pan, Hao Chen, Hongwei Liu
In 2020, Cao et al. proved that any repeated-root constacyclic code is monomially equivalent to a matrix product code of simple-root constacyclic codes. In this paper, we study a family of matrix product codes with wonderful properties, which is a generalization of linear codes obtained from the \([u+v|u-v]\)-construction and \([u+v|\lambda ^{-1}u-\lambda ^{-1}v]\)-construction. Then we show that any
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Some constacyclic BCH codes with good parameters Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-07-02 Jin Li, Huilian Zhu, Shan Huang
BCH codes as a subclass of constacyclic BCH codes have been widely studied, while the results on the parameters of BCH codes over finite fields are still very limited. In this paper, we investigate some q-ary BCH codes and \(\lambda \)-constacyclic BCH codes of length \(q^{m}+1\), where q is a prime power and \(\textrm{ord}(\lambda )\mid q-1\). We determine the dimensions of these codes with some large
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Constructions for t-designs and s-resolvable t-designs Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-27 Tran van Trung
The purpose of the present paper is to introduce recursive methods for constructing simple t-designs, s-resolvable t-designs, and large sets of t-designs. The results turn out to be very effective for finding these objects. In particular, they reveal a fundamental property of the considered designs. Consequently, many new infinite series of simple t-designs, t-designs with s-resolutions and large sets
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Security analysis of the ISO standard $$\textsf{OFB}$$ - $$\textsf{DRBG}$$ Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-27 Woohyuk Chung, Hwigyeom Kim, Jooyoung Lee, Yeongmin Lee
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A survey of compositional inverses of permutation polynomials over finite fields Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-27 Qiang Wang
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Finding orientations of supersingular elliptic curves and quaternion orders Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-26 Sarah Arpin, James Clements, Pierrick Dartois, Jonathan Komada Eriksen, Péter Kutas, Benjamin Wesolowski
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Affine vector space partitions and spreads of quadrics Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-27 Somi Gupta, Francesco Pavese
An affine spread is a set of subspaces of \(\textrm{AG}(n, q)\) of the same dimension that partitions the points of \(\textrm{AG}(n, q)\). Equivalently, an affine spread is a set of projective subspaces of \(\textrm{PG}(n, q)\) of the same dimension which partitions the points of \(\textrm{PG}(n, q) \setminus H_{\infty }\); here \(H_{\infty }\) denotes the hyperplane at infinity of the projective closure
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On the maximum size of variable-length non-overlapping codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-25 Geyang Wang, Qi Wang
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The existence of $$(\mathbb {Z}_v,4,1)$$ -disjoint difference families Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-20 Xinyue Ming, Tao Feng, Guojing Jia, Xiaomiao Wang
This paper shows that a \((\mathbb {Z}_v,4,1)\)-disjoint difference family exists if and only if \(v\equiv 1\pmod {12}\) and \(v\ne 25\) by giving suitable translations of base blocks of a \((\mathbb {Z}_v,4,1)\)-cyclic difference family. The Combinatorial Nullstellensatz finds its application in constructing disjoint difference families.
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Multivariate correlation attacks and the cryptanalysis of LFSR-based stream ciphers Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-18 Isaac A. Canales-Martínez, Igor Semaev
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New families of quaternionic Hadamard matrices Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-18 Santiago Barrera Acevedo, Heiko Dietrich, Corey Lionis
A quaternionic Hadamard matrix (QHM) of order n is an \(n\times n\) matrix H with non-zero entries in the quaternions such that \(HH^*=nI_n\), where \(I_n\) and \(H^*\) denote the identity matrix and the conjugate-transpose of H, respectively. A QHM is dephased if all the entries in its first row and first column are 1, and it is non-commutative if its entries generate a non-commutative group. The
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Bases for Riemann–Roch spaces of linearized function fields with applications to generalized algebraic geometry codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-15 Horacio Navarro
Several applications of function fields over finite fields, or equivalently, algebraic curves over finite fields, require computing bases for Riemann–Roch spaces. In this paper, we determine explicit bases for Riemann–Roch spaces of linearized function fields, and we give a lower bound for the minimum distance of generalized algebraic geometry codes. As a consequence, we construct generalized algebraic
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Optimal ternary locally repairable codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-13 Jie Hao, Shu-Tao Xia, Kenneth W. Shum, Bin Chen, Fang-Wei Fu, Yixian Yang
Locally repairable codes (LRCs) are linear codes with locality properties for code symbols, which have important applications in distributed storage systems. In this paper, we completely classify all the possible code parameters of optimal ternary LRCs achieving the Singleton-like bound proposed by Gopalan et al. Explicit constructions of optimal ternary LRCs are given for each group of possible code
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Circular external difference families: construction and non-existence Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-12 Huawei Wu, Jing Yang, Keqin Feng
The circular external difference family and its strong version are of great significance both in theory and in applications. In this paper, we apply the classical cyclotomic construction to the circular external differnece family and exhibit several concrete examples, in particular constructing an infinite family. Furthermore, we prove that all strong circular external differnece families are constructed
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An asymptotic property of quaternary additive codes Des. Codes Cryptogr. (IF 1.4) Pub Date : 2024-06-12 Jürgen Bierbrauer, Stefano Marcugini, Fernanda Pambianco
Let \(n_k(s)\) be the maximal length n such that a quaternary additive \([n,k,n-s]_4\)-code exists. We solve a natural asymptotic problem by determining the lim sup \(\lambda _k\) of \(n_k(s)/s\) for s going to infinity, and the smallest value of s such that \(n_k(s)/s=\lambda _k.\) Our new family of quaternary additive codes has parameters \([4^k-1,k,4^k-4^{k-1}]_4=[2^{2k}-1,k,3\cdot 2^{2k-2}]_4\)