Designs, Codes and Cryptography最新文献_第8页

Curve-lifted codes for local recovery using lines 利用线路进行局部恢复的曲线提升代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-17 DOI: 10.1007/s10623-024-01456-0

Gretchen L. Matthews, Travis Morrison, Aidan W. Murphy

引用次数: 0

Hulls of cyclic codes with respect to the regular permutation inner product 与正则置换内积有关的循环码的赫尔

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-15 DOI: 10.1007/s10623-024-01428-4

Xiaoshan Quan, Qin Yue, Fuqing Sun

引用次数: 0

Explicit constructions of NMDS self-dual codes NMDS 自偶码的显式构造

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-12 DOI: 10.1007/s10623-024-01450-6

Dongchun Han, Hanbin Zhang

引用次数: 0

New spence difference sets 新的斯彭斯差异套装

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-10 DOI: 10.1007/s10623-024-01446-2

James A. Davis, John Polhill, Ken Smith, Eric Swartz, Jordan Webster

{"title":"New spence difference sets","authors":"James A. Davis, John Polhill, Ken Smith, Eric Swartz, Jordan Webster","doi":"10.1007/s10623-024-01446-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01446-2","url":null,"abstract":"Spence [9] constructed (left( frac{3^{d+1}(3^{d+1}-1)}{2}, frac{3^d(3^{d+1}+1)}{2}, frac{3^d(3^d+1)}{2}right) )-difference sets in groups (K times C_3^{d+1}) for d any positive integer and K any group of order (frac{3^{d+1}-1}{2}). Smith and Webster [8] have exhaustively studied the (d=1) case without requiring that the group have the form listed above and found many constructions. Among these, one intriguing example constructs Spence difference sets in (A_4 times C_3) by using (3, 3, 3, 1)-relative difference sets in a non-normal subgroup isomorphic to (C_3^2). Drisko [3] has a note implying that his techniques allow constructions of Spence difference sets in groups with a noncentral normal subgroup isomorphic to (C_3^{d+1}) as long as (frac{3^{d+1}-1}{2}) is a prime power. We generalize this result by constructing Spence difference sets in similar families of groups, but we drop the requirement that (frac{3^{d+1}-1}{2}) is a prime power. We conjecture that any group of order (frac{3^{d+1}(3^{d+1}-1)}{2}) with a normal subgroup isomorphic to (C_3^{d+1}) will have a Spence difference set (this is analogous to Dillon’s conjecture in 2-groups, and that result was proved in Drisko’s work). Finally, we present the first known example of a Spence difference set in a group where the Sylow 3-subgroup is nonabelian and has exponent bigger than 3. This new construction, found by computing the full automorphism group (textrm{Aut}(mathcal {D})) of a symmetric design associated to a known Spence difference set and identifying a regular subgroup of (textrm{Aut}(mathcal {D})), uses (3, 3, 3, 1)-relative difference sets to describe the difference set.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Vectorial negabent concepts: similarities, differences, and generalizations 矢量否定概念：相似性、差异性和概括性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-05 DOI: 10.1007/s10623-024-01454-2

Nurdagül Anbar, Sadmir Kudin, Wilfried Meidl, Enes Pasalic, Alexandr Polujan

{"title":"Vectorial negabent concepts: similarities, differences, and generalizations","authors":"Nurdagül Anbar, Sadmir Kudin, Wilfried Meidl, Enes Pasalic, Alexandr Polujan","doi":"10.1007/s10623-024-01454-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01454-2","url":null,"abstract":"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 is extended to generalized Boolean functions from ({mathbb {F}}_2^n) to the cyclic group ({mathbb {Z}}_{2^k}). It is shown how to obtain nega-({mathbb {Z}}_{2^k})-bent functions from ({mathbb {Z}}_{2^k})-bent functions, or equivalently, corresponding non-splitting relative difference sets from the splitting relative difference sets. This generalizes the shifting results for Boolean bent and negabent functions. We finally point to constructions of ({mathbb {Z}}_8)-bent functions employing permutations with the (({mathcal {A}}_m)) property, and more generally we show that the inverse permutation gives rise to ({mathbb {Z}}_{2^k})-bent functions.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141545935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Additivity of symmetric and subspace 2-designs 对称和子空间 2 设计的可加性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-05 DOI: 10.1007/s10623-024-01452-4

Marco Buratti, Anamari Nakić

引用次数: 0

Around LCD group codes 围绕 LCD 组代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-05 DOI: 10.1007/s10623-024-01451-5

Javier de la Cruz, Wolfgang Willems

引用次数: 0

Some self-dual codes and isodual codes constructed by matrix product codes 由矩阵乘积码构建的一些自偶码和等偶码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-04 DOI: 10.1007/s10623-024-01453-3

Xu Pan, Hao Chen, Hongwei Liu

{"title":"Some self-dual codes and isodual codes constructed by matrix product codes","authors":"Xu Pan, Hao Chen, Hongwei Liu","doi":"10.1007/s10623-024-01453-3","DOIUrl":"https://doi.org/10.1007/s10623-024-01453-3","url":null,"abstract":"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 (lambda )-constacyclic code (not necessary repeated-root (lambda )-constacyclic code) of length N over the finite field (mathbb {F}_q) with (textrm{gcd}(frac{q-1}{textrm{ord}(lambda )},N)ge 2), where (textrm{ord}(lambda )) is the order of (lambda ) in the cyclic group (mathbb {F}^*_q=mathbb {F}_qbackslash {0}), is a matrix product code of some constacyclic codes. It is a highly interesting question that the existence of sequences ({C_1,C_2,C_3,...}) of Euclidean (or Hermitian) self-dual codes with square-root-like minimum Hamming distances, i.e., (C_i) is an ([n(C_i),k(C_i),d(C_i)]_q)-linear code such that $$begin{aligned} lim _{irightarrow +infty }n(C_i)=+infty ,,,,,text {and},,,,,lim _{irightarrow +infty }frac{d(C_i)}{sqrt{n(C_i)}}>0. end{aligned}$$Based on the ([u+v|lambda ^{-1}u-lambda ^{-1}v])-construction, we construct several families of Euclidean (or Hermitian) self-dual codes with square-root-like minimum Hamming distances by using Reed-Muller codes, projective Reed-Muller codes. And we construct some new Euclidean isodual (lambda )-constacyclic codes with square-root-like minimum Hamming distances from Euclidean self-dual cyclic codes and Euclidean self-dual negacyclic codes by monomial equivalences.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Some constacyclic BCH codes with good parameters 一些参数良好的常环 BCH 编码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-07-02 DOI: 10.1007/s10623-024-01433-7

Jin Li, Huilian Zhu, Shan Huang

引用次数: 0

A survey of compositional inverses of permutation polynomials over finite fields 有限域上置换多项式的组成逆的考察

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-06-27 DOI: 10.1007/s10623-024-01436-4

Qiang Wang

引用次数: 0