Designs, Codes and Cryptography最新文献_第9页

Several new classes of optimal ternary cyclic codes with two or three zeros 几种新的具有两个或三个零的最优三元循环码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-19 DOI: 10.1007/s10623-024-01541-4

Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang

{"title":"Several new classes of optimal ternary cyclic codes with two or three zeros","authors":"Gaofei Wu, Zhuohui You, Zhengbang Zha, Yuqing Zhang","doi":"10.1007/s10623-024-01541-4","DOIUrl":"https://doi.org/10.1007/s10623-024-01541-4","url":null,"abstract":"Cyclic codes are a subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics due to their efficient encoding and decoding algorithms. Let (alpha ) be a generator of (mathbb F_{3^m}setminus {0}), where m is a positive integer. Denote by (mathcal {C}_{(i_1,i_2,cdots , i_t)}) the cyclic code with generator polynomial (m_{alpha ^{i_1}}(x)m_{alpha ^{i_2}}(x)cdots m_{alpha ^{i_t}}(x)), where ({{m}_{alpha ^{i}}}(x)) is the minimal polynomial of ({{alpha }^{i}}) over ({{mathbb {F}}_{3}}). In this paper, by analyzing the solutions of certain equations over finite fields, we present four classes of optimal ternary cyclic codes (mathcal {C}_{(0,1,e)}) and (mathcal {C}_{(1,e,s)}) with parameters ([3^m-1,3^m-frac{3m}{2}-2,4]), where (s=frac{3^m-1}{2}). In addition, by determining the solutions of certain equations and analyzing the irreducible factors of certain polynomials over (mathbb F_{3^m}), we present four classes of optimal ternary cyclic codes (mathcal {C}_{(2,e)}) and (mathcal {C}_{(1,e)}) with parameters ([3^m-1,3^m-2m-1,4]). We show that our new optimal cyclic codes are not covered by known ones.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"24 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142858387","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

Quantum security of Trojan message attacks on Merkle–Damgård hash construction 基于merkle - damg<s:1> rd哈希构造的木马消息攻击的量子安全性

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-18 DOI: 10.1007/s10623-024-01538-z

Ying Xu, Xiaoni Du, Jian Zou

引用次数: 0

Optimal combinatorial neural codes via symmetric designs 通过对称设计的最优组合神经编码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-18 DOI: 10.1007/s10623-024-01534-3

Xingyu Zheng, Shukai Wang, Cuiling Fan

引用次数: 0

Relating code equivalence to other isomorphism problems 将代码等价与其他同构问题联系起来

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-16 DOI: 10.1007/s10623-024-01542-3

Huck Bennett, Kaung Myat Htay Win

引用次数: 0

Hulls of projective Reed–Muller codes 射影里德-穆勒码的船体

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-14 DOI: 10.1007/s10623-024-01543-2

Nathan Kaplan, Jon-Lark Kim

引用次数: 0

On set systems with strongly restricted intersections 在具有强约束交叉口的集合系统上

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-05 DOI: 10.1007/s10623-024-01535-2

Xin Wei, Xiande Zhang, Gennian Ge

{"title":"On set systems with strongly restricted intersections","authors":"Xin Wei, Xiande Zhang, Gennian Ge","doi":"10.1007/s10623-024-01535-2","DOIUrl":"https://doi.org/10.1007/s10623-024-01535-2","url":null,"abstract":"Set systems with strongly restricted intersections, called (alpha )-intersecting families for a vector (alpha ), were introduced recently as a generalization of several well-studied intersecting families including the classical oddtown and eventown. Given a binary vector (alpha =(a_1, ldots , a_k)), a collection ({mathcal {F}}) of subsets over an n element set is an (alpha )-intersecting family modulo 2 if for each (i=1,2,ldots ,k), all i-wise intersections of distinct members in ({mathcal {F}}) have sizes with the same parity as (a_i). Let (f_alpha (n)) denote the maximum size of such a family. In this paper, we study the asymptotic behavior of (f_alpha (n)) when n goes to infinity. We show that if t is the maximum integer such that (a_t=1) and (2tle k), then (f_alpha (n)sim (t! n)^{1/t}). More importantly, we show that for any constant (c>0), as the length k goes larger, (f_alpha (n)) is upper bounded by (O (n^c)) for almost all (alpha ). Equivalently, no matter what k is, there are only finitely many (alpha ) satisfying (f_alpha (n)=Omega (n^c)). This answers an open problem raised by Johnston and O’Neill in 2023. All of our results can be generalized to modulo p setting for any prime p smoothly.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"37 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142776806","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 3-dimensional MRD codes of type $$langle X^{q^t},X+delta X^{q^{2t}},G(X) rangle $$ 论型的三维MRD码 $$langle X^{q^t},X+delta X^{q^{2t}},G(X) rangle $$

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-05 DOI: 10.1007/s10623-024-01528-1

Daniele Bartoli, Francesco Ghiandoni

引用次数: 0

Derivative descendants of cyclic codes and constacyclic codes 循环码和恒循环码的派生后代

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01536-1

Li Xu, Cuiling Fan, Chunming Tang, Zhengchun Zhou

引用次数: 0

Codes over $$mathbb {F}_4$$ and $$mathbb {F}_2 times mathbb {F}_2$$ and theta series of the corresponding lattices in quadratic fields 二次域中对应格的$$mathbb {F}_4$$和$$mathbb {F}_2 times mathbb {F}_2$$上的代码和级数

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01537-0

Josline Freed

引用次数: 0

A pair of orthogonal orthomorphisms of finite nilpotent groups 有限幂零群的一对正交正胚

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-04 DOI: 10.1007/s10623-024-01540-5

Shikang Yu, Tao Feng, Menglong Zhang

引用次数: 0