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Balanced reconstruction codes for single edits Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-03-16
Abstract 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
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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
Abstract Starting from the problem of d-tensor isomorphism (d- \(\textsf {TI}\) ), we study the relation between various code equivalence problems in different metrics. In particular, we show a reduction from the sum-rank metric ( \(\textsf {CE}_{\textsf {sr}}\) ) to the rank metric ( \(\textsf {CE}_{\textsf {rk}}\) ). To obtain this result, we investigate reductions between tensor problems. We define
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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
Abstract In this paper, we first consider the existence conditions, the construction and the enumeration of Hermitian self-dual \(\theta \) -cyclic and \(\theta \) -negacyclic codes over \(\mathrm{I\hspace{-2.10007pt}F}_{p^2}\) , where p is a prime number and \(\theta \) is the Frobenius automorphism over \(\mathrm{I\hspace{-2.10007pt}F}_{p^2}\) . We then give necessary and sufficient conditions for
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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
Abstract Fractional repetition codes (FRCs) are a special family of storage codes with the repair-by-transfer property in distributed storage systems. Constructions of FRCs are naturally related to combinatorial designs, graphs, and hypergraphs. In this paper, we consider an extremal problem on regular graphs related to FRCs where each packet is stored on \(\rho =2\) nodes. The problem asks for the
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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
Abstract The Mixed Integer Linear Programming (MILP) technique has been widely applied in the realm of symmetric-key cryptanalysis. In this paper, we propose a new bitwise breakdown MILP modeling strategy for describing the linear propagation rules of modular addition-based operations. We apply such new techniques to cryptanalysis of the SNOW stream cipher family and find new linear masks: we use the
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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
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In search of maximum non-overlapping codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08 Lidija Stanovnik, Miha Moškon, Miha Mraz
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Hardness estimates of the code equivalence problem in the rank metric Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08
Abstract In this paper, we analyze the hardness of the Matrix Code Equivalence (MCE) problem for matrix codes endowed with the rank metric, and provide the first algorithms for solving it. We do this by making a connection to another well-known equivalence problem from multivariate cryptography—the Isomorphism of Polynomials (IP). Under mild assumptions, we give tight reductions from MCE to the homogenous
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New constructions of constant dimension subspace codes with large sizes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-08 Yun Li, Hongwei Liu, Sihem Mesnager
Subspace codes have important applications in random network coding. It is a classical problem to construct subspace codes where both their size and their minimum distance are as large as possible. In particular, cyclic constant dimension subspace codes have additional properties which can be used to make encoding and decoding more efficient. In this paper, we construct large cyclic constant dimension
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Improved bounds for codes correcting insertions and deletions Des. Codes Cryptogr. (IF 1.6) Pub Date : 2024-01-07 Kenji Yasunaga
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Strongly regular graphs decomposable into a divisible design graph and a Hoffman coclique Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-29 Alexander L. Gavrilyuk, Vladislav V. Kabanov
In 2022, the second author found a prolific construction of strongly regular graphs, which is based on joining a coclique and a divisible design graph with certain parameters. The construction produces strongly regular graphs with the same parameters as the complement of the symplectic graph \(\textsf{Sp}(2d,q)\). In this paper, we determine the parameters of strongly regular graphs which admit a decomposition
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Introducing nega-Forrelation: quantum algorithms in analyzing nega-Hadamard and nega-crosscorrelation spectra Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 Suman Dutta, Subhamoy Maitra
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On a class of permutation rational functions involving trace maps Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27
Abstract Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on extensions of finite fields, especially for the cases of quadratic and cubic extensions. Our achievements are obtained by investigating absolute irreducibility
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Harmonic Tutte polynomials of matroids II Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 Thomas Britz, Himadri Shekhar Chakraborty, Reina Ishikawa, Tsuyoshi Miezaki, Hopein Christofen Tang
In this work, we introduce the harmonic generalization of the m-tuple weight enumerators of codes over finite Frobenius rings. A harmonic version of the MacWilliams-type identity for m-tuple weight enumerators of codes over finite Frobenius ring is also given. Moreover, we define the demi-matroid analogue of well-known polynomials from matroid theory, namely Tutte polynomials and coboundary polynomials
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On the (in)security of optimized Stern-like signature schemes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-27 André Chailloux, Simona Etinski
Stern’s signature scheme is a historically important code-based signature scheme. A crucial optimization of this scheme is to generate pseudo-random vectors and permutation instead of random ones, and most proposals that are based on Stern’s signature use this optimization. However, its security has not been properly analyzed, especially when we use deterministic commitments. In this article, we study
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Construction of self-orthogonal $$\mathbb {Z}_{2^k}$$ -codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-19
Abstract In this paper we give three constructions of cyclic self-orthogonal codes over \(\mathbb {Z}_{2^k}\) , for \(k\ge 3,\) from Boolean functions on n variables. The first construction for each k, \(3\le k\le n,\) yields a self-orthogonal \(\mathbb {Z}_{2^k}\) -code of length \(2^{n+2}\) with all Euclidean weights divisible by \(2^{k+1}.\) In the remaining two constructions, for each even n and
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Weierstrass semigroups, pure gaps and codes on function fields Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-19 Alonso S. Castellanos, Erik A. R. Mendoza, Luciane Quoos
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Optimal binary and ternary locally repairable codes with minimum distance 6 Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-15 Wenqin Zhang, Yuan Luo, Lele Wang
A locally repairable code (LRC) is a code that can recover any symbol of a codeword by reading at most \(r \) other symbols, denoted by \(r \)-LRC. In this paper, we study binary and ternary linear LRCs with disjoint repair groups and minimum distance \(d \) = 6. Using the intersection subspaces technique, we explicitly construct dimensional optimal LRCs. First, based on the intersection subspaces
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Codes on subgroups of weighted projective tori Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-09 Mesut Şahin, Oğuz Yayla
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Observations on the branch number and differential analysis of SPEEDY Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-08 Lei Zhang
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LowMS: a new rank metric code-based KEM without ideal structure Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-07 Nicolas Aragon, Victor Dyseryn, Philippe Gaborit, Pierre Loidreau, Julian Renner, Antonia Wachter-Zeh
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Decreasing norm-trace codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-06 Cícero Carvalho, Hiram H. López, Gretchen L. Matthews
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Hulls of linear codes from simplex codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-06 Guangkui Xu, Gaojun Luo, Xiwang Cao, Heqian Xu
The hull of a linear code plays an important role in determining the complexity of algorithms for checking permutation equivalence of two linear codes and computing the automorphism group of a linear code. Regarding the quantum error correction, linear codes with determined hull are used to construct quantum codes. In this paper, we focus on the hull of Simplex codes and punctured Simplex codes. We
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Improved bounds for permutation arrays under Chebyshev distance Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-12-06 Sergey Bereg, Mohammadreza Haghpanah, Brian Malouf, I. Hal Sudborough
Permutation arrays under the Chebyshev metric have been considered for error correction in noisy channels. Let P(n, d) denote the maximum size of any array of permutations on n symbols with pairwise Chebyshev distance d. We give new techniques and improved upper and lower bounds on P(n, d), including a precise formula for P(n, 2).
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Dynamics of polynomial maps over finite fields Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-30 José Alves Oliveira, F. E. Brochero Martínez
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Jacobi sums over Galois rings of arbitrary characters and their applications in constructing asymptotically optimal codebooks Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-28 Deng-Ming Xu, Gang Wang, Sihem Mesnager, You Gao, Fang-Wei Fu
Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in multiple access communication systems in code division. Firstly, this paper studies the Jacobi sums over Galois rings of arbitrary characteristics and completely determines their absolute values. This extends the work by Li et al. (Sci China 56(7):1457–1465, 2013), where the Jacobi
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Improved meet-in-the-middle attack on 10 rounds of the AES-256 block cipher Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-24 Jiqiang Lu, Wenchang Zhou
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$$\varepsilon $$ -Almost collision-flat universal hash functions and mosaics of designs Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-18 Moritz Wiese, Holger Boche
We introduce, motivate and study \(\varepsilon \)-almost collision-flat universal (ACFU) hash functions \(f:\mathcal X\times \mathcal S\rightarrow \mathcal A\). Their main property is that the number of collisions in any given value is bounded. Each \(\varepsilon \)-ACFU hash function is an \(\varepsilon \)-almost universal (AU) hash function, and every \(\varepsilon \)-almost strongly universal (ASU)
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On the equivalence of $$\mathbb {Z}_{p^s}$$ -linear generalized Hadamard codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-18 Dipak K. Bhunia, Cristina Fernández-Córdoba, Carlos Vela, Mercè Villanueva
Linear codes of length n over \(\mathbb {Z}_{p^s}\), p prime, called \(\mathbb {Z}_{p^s}\)-additive codes, can be seen as subgroups of \(\mathbb {Z}_{p^s}^n\). A \(\mathbb {Z}_{p^s}\)-linear generalized Hadamard (GH) code is a GH code over \(\mathbb {Z}_p\) which is the image of a \(\mathbb {Z}_{p^s}\)-additive code under a generalized Gray map. It is known that the dimension of the kernel allows to
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On the 430-cap of $$\textrm{PG}(6,4)$$ having two intersection sizes with respect to hyperplanes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-18 John Bamberg
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Fast Kötter–Nielsen–Høholdt interpolation over skew polynomial rings and its application in coding theory Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-18 Hannes Bartz, Thomas Jerkovits, Johan Rosenkilde
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Lattice codes for lattice-based PKE Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-16 Shanxiang Lyu, Ling Liu, Cong Ling, Junzuo Lai, Hao Chen
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Unconditionally secure non-malleable secret sharing and circular external difference families Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-16 Shannon Veitch, Douglas R. Stinson
Various notions of non-malleable secret sharing schemes have been considered. In this paper, we review the existing work on non-malleable secret sharing and suggest a novel game-based definition. We provide a new construction of an unconditionally secure non-malleable threshold scheme with respect to a specified relation. To do so, we introduce a new type of algebraic manipulation detection code and
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Jacobi polynomials and harmonic weight enumerators of the first-order Reed–Muller codes and the extended Hamming codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-16 Tsuyoshi Miezaki, Akihiro Munemasa
In the present paper, we give harmonic weight enumerators and Jacobi polynomials for the first-order Reed–Muller codes and the extended Hamming codes. As a corollary, we show the nonexistence of combinatorial 4-designs in these codes.
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On the image of an affine subspace under the inverse function within a finite field Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-16 Nikolay Kolomeec, Denis Bykov
We consider the function \(x^{-1}\) that inverses a finite field element \(x \in \mathbb {F}_{p^n}\) (p is prime, \(0^{-1} = 0\)) and affine \(\mathbb {F}_{p}\)-subspaces of \(\mathbb {F}_{p^n}\) such that their images are affine subspaces as well. It is proved that the image of an affine subspace L, \(|L |> 2\), is an affine subspace if and only if \(L = s\mathbb {F}_{p^k}\), where \(s\in \mathbb
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Determination of the sizes of optimal geometric orthogonal codes with parameters $$(n\times m,k,\lambda ,k-1)$$ Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-16 Xiaowei Su, Zihong Tian, Guohui Hao
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Mutually disjoint Steiner systems from BCH codes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-14 Qianqian Yan, Junling Zhou
Liu et al. (IEEE Trans Inf Theory 68:3096–3107, 2022) investigated a class of BCH codes \(\mathcal {C}_{(q,q+1,\delta ,1)}\) with \(q=\delta ^m\) a prime power and proved that the set \(\mathcal {B}_{\delta +1}\) of supports of the minimum weight codewords supports a Steiner system \({{\text {S}}}(3,\delta +1,q+1)\). In this paper, we give an equivalent formulation of \(\mathcal {B}_{\delta +1}\) in
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On maximal partial Latin hypercubes Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-14 Diane M. Donovan, Mike J. Grannell, Emine Şule Yazıcı
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Provable lattice reduction of $$\mathbb {Z}^n$$ with blocksize n/2 Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-11 Léo Ducas
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New classes of NMDS codes with dimension 3 Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-02 Cuiling Fan, An Wang, Li Xu
The singleton defect of an [n, k, d] linear code \(\mathcal{C}\) is defined as \(s(\mathcal{C})=n-k+1-d\). Codes with \(s({\mathcal {C}})=s({\mathcal {C}}^{\bot })=1\) are called near maximum distance separable (NMDS) codes. It is known that an \([n,3,n-3]\) NMDS code is equivalent to an (n, 3)-arc in PG(2, q). In this paper, by adding some suitable projective points into some known \((q+5,3)\)-arcs
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Codes with respect to weighted poset block metric Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-11-02 Wen Ma, Jinquan Luo
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Construction and enumeration of self-orthogonal and self-dual codes over Galois rings of even characteristic Des. Codes Cryptogr. (IF 1.6) Pub Date : 2023-10-27 Monika Yadav, Anuradha Sharma