Designs, Codes and Cryptography最新文献

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

Moments of autocorrelation demerit factors of binary sequences 二进制序列自相关扣分因子的矩

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-01 DOI: 10.1007/s10623-024-01482-y

Daniel J. Katz, Miriam E. Ramirez

{"title":"Moments of autocorrelation demerit factors of binary sequences","authors":"Daniel J. Katz, Miriam E. Ramirez","doi":"10.1007/s10623-024-01482-y","DOIUrl":"https://doi.org/10.1007/s10623-024-01482-y","url":null,"abstract":"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. We consider the uniform probability measure on the (2^ell ) binary sequences of length (ell ) and investigate the distribution of the demerit factors of these sequences. Sarwate and Jedwab have respectively calculated the mean and variance of this distribution. We develop new combinatorial techniques to calculate the pth central moment of the demerit factor for binary sequences of length (ell ). These techniques prove that for (pge 2) and (ell ge 4), all the central moments are strictly positive. For any given p, one may use the technique to obtain an exact formula for the pth central moment of the demerit factor as a function of the length (ell ). Jedwab’s formula for variance is confirmed by our technique with a short calculation, and we go beyond previous results by also deriving an exact formula for the skewness. A computer-assisted application of our method also obtains exact formulas for the kurtosis, which we report here, as well as the fifth central moment.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2024-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142100952","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

Storage codes and recoverable systems on lines and grids 线路和电网上的存储代码和可恢复系统

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-09-01 DOI: 10.1007/s10623-024-01481-z

Alexander Barg, Ohad Elishco, Ryan Gabrys, Geyang Wang, Eitan Yaakobi

引用次数: 0