Designs, Codes and Cryptography最新文献_第4页

On Abelian one-dimensional hull codes in group algebras 论群代数中的阿贝尔一维船体码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-10-03 DOI: 10.1007/s10623-024-01504-9

Rong Luo, Mingliang Yan, Sihem Mesnager, Dongchun Han

{"title":"On Abelian one-dimensional hull codes in group algebras","authors":"Rong Luo, Mingliang Yan, Sihem Mesnager, Dongchun Han","doi":"10.1007/s10623-024-01504-9","DOIUrl":"https://doi.org/10.1007/s10623-024-01504-9","url":null,"abstract":"This paper focuses on hull dimensional codes obtained by the intersection of linear codes and their dual. These codes were introduced by Assmus and Key and have been the subject of significant theoretical and practical research over the years, gaining increased attention in recent years. Let (mathbb {F}_q) denote the finite field with q elements, and let G be a finite Abelian group of order n. The paper investigates Abelian codes defined as ideals of the group algebra (mathbb {F}_qG) with coefficients in (mathbb {F}_q). Specifically, it delves into Abelian hull dimensional codes in the group algebra (mathbb {F}_qG), where G is a finite Abelian group of order n with (gcd (n,q)=1). Specifically, we first examine general hull Abelian codes and then narrow its focus to Abelian one-dimensional hull codes. Next, we focus on Abelian one-dimensional hull codes and present some necessary and sufficient conditions for characterizing them. Consequently, we generalize a recent result on Abelian codes and show that no binary or ternary Abelian codes with one-dimensional hulls exist. Furthermore, we construct Abelian codes with one-dimensional hulls by generating idempotents, derive optimal ones with one-dimensional hulls, and establish several existing results of Abelian codes with one-dimensional hulls. Finally, we develop enumeration results through a simple formula that counts Abelian codes with one-dimensional hulls in (mathbb {F}_qG). These achievements exploit the rich algebraic structure of those Abelian codes and enhance and increase our knowledge of them by considering their hull dimensions, reducing the gap between their interests and our understanding of them.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142374109","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

Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions 基于扩展布尔函数的渐近最优非周期性准互补序列集

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-28 DOI: 10.1007/s10623-024-01501-y

Bingsheng Shen, Tao Yu, Zhengchun Zhou, Yang Yang

引用次数: 0

Non-linear MRD codes from cones over exterior sets 来自外部集合锥体的非线性 MRD 代码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-18 DOI: 10.1007/s10623-024-01492-w

Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi

{"title":"Non-linear MRD codes from cones over exterior sets","authors":"Nicola Durante, Giovanni Giuseppe Grimaldi, Giovanni Longobardi","doi":"10.1007/s10623-024-01492-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01492-w","url":null,"abstract":"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 n-1). A code of this class ({mathcal {C}}_{sigma ,T}), where (1in T subseteq {mathbb {F}}_q^*) and (sigma ) is a generator of (textrm{Gal}({mathbb {F}}_{q^n}|{mathbb {F}}_q)), arises from a cone of ({textrm{PG}}(n-1,q^n)) with vertex an ((n-d-2))-dimensional subspace over a maximum exterior set ({mathcal {E}}) with respect to (Omega _{d-2}(Gamma )). We prove that the codes introduced in Cossidente et al (Des Codes Cryptogr 79:597–609, 2016), Donati and Durante (Des Codes Cryptogr 86:1175–1184, 2018), Durante and Siciliano (Electron J Comb, 2017) are suitable punctured ones of ({mathcal {C}}_{sigma ,T}) and we solve completely the inequivalence issue for this class showing that ({mathcal {C}}_{sigma ,T}) is neither equivalent nor adjointly equivalent to the non-linear MRD codes ({mathcal {C}}_{n,k,sigma ,I}), (I subseteq {mathbb {F}}_q), obtained in Otal and Özbudak (Finite Fields Appl 50:293–303, 2018).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142245509","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

Arithmetization-oriented APN permutations 面向算术的 APN 排列

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-18 DOI: 10.1007/s10623-024-01487-7

Lilya Budaghyan, Mohit Pal

引用次数: 0

A common generalization of hypercube partitions and ovoids in polar spaces 极地空间中的超立方体分区和卵形体的通用概括

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-17 DOI: 10.1007/s10623-024-01489-5

Jozefien D’haeseleer, Ferdinand Ihringer, Kai-Uwe Schmidt

引用次数: 0

Capacity of an infinite family of networks related to the diamond network for fixed alphabet sizes 在字母大小固定的情况下，与钻石网络相关的无限网络族的容量

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-17 DOI: 10.1007/s10623-024-01485-9

Sascha Kurz

引用次数: 0

Designs in finite classical polar spaces 有限经典极空间中的设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-17 DOI: 10.1007/s10623-024-01491-x

Michael Kiermaier, Kai-Uwe Schmidt, Alfred Wassermann

{"title":"Designs in finite classical polar spaces","authors":"Michael Kiermaier, Kai-Uwe Schmidt, Alfred Wassermann","doi":"10.1007/s10623-024-01491-x","DOIUrl":"https://doi.org/10.1007/s10623-024-01491-x","url":null,"abstract":"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 of the polar space. The first nontrivial such designs for (t > 1) were found by De Bruyn and Vanhove in 2012, and some more designs appeared recently in the PhD thesis of Lansdown. In this article, we investigate the theory of classical and subspace designs for applicability to designs in polar spaces, explicitly allowing arbitrary block dimensions. In this way, we obtain divisibility conditions on the parameters, derived and residual designs, intersection numbers and an analog of Fisher’s inequality. We classify the parameters of symmetric designs. Furthermore, we conduct a computer search to construct designs of strength (t=2), resulting in designs for more than 140 previously unknown parameter sets in various classical polar spaces over (mathbb {F}_2) and (mathbb {F}_3).","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142235130","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

On the uniqueness of balanced complex orthogonal design 论平衡复正交设计的唯一性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-03 DOI: 10.1007/s10623-024-01483-x

Yiwen Gao, Yuan Li, Haibin Kan

引用次数: 0

Minimal abundant packings and choosability with separation 最少的丰富包装和分离的可选择性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-03 DOI: 10.1007/s10623-024-01484-w

Zoltán Füredi, Alexandr Kostochka, Mohit Kumbhat

{"title":"Minimal abundant packings and choosability with separation","authors":"Zoltán Füredi, Alexandr Kostochka, Mohit Kumbhat","doi":"10.1007/s10623-024-01484-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01484-w","url":null,"abstract":"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 minimum (v=v_0(k,t)) when abundant packings exist. For a graph G and a positive integer c, let (chi _ell (G,c)) be the minimum value of k such that one can properly color the vertices of G from any assignment of lists L(v) such that (|L(v)|=k) for all (vin V(G)) and (|L(u)cap L(v)|le c) for all (uvin E(G)). Kratochvíl, Tuza and Voigt in 1998 asked to determine (lim _{nrightarrow infty } chi _ell (K_n,c)/sqrt{cn}) (if it exists). Using our bound on (v_0(k,t)), we prove that the limit exists and equals 1. Given c, we find the exact value of (chi _ell (K_n,c)) for infinitely many n.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142123908","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

Bandersnatch: a fast elliptic curve built over the BLS12-381 scalar field Bandersnatch：在 BLS12-381 标量场上构建的快速椭圆曲线

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-01 DOI: 10.1007/s10623-024-01472-0

Simon Masson, Antonio Sanso, Zhenfei Zhang

引用次数: 0