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

The support designs of several families of lifted linear codes 几种提升线性码族的支撑设计

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-25 DOI: 10.1007/s10623-024-01549-w

Cunsheng Ding, Zhonghua Sun, Qianqian Yan

{"title":"The support designs of several families of lifted linear codes","authors":"Cunsheng Ding, Zhonghua Sun, Qianqian Yan","doi":"10.1007/s10623-024-01549-w","DOIUrl":"https://doi.org/10.1007/s10623-024-01549-w","url":null,"abstract":"A generator matrix of a linear code ({mathcal {C}}) over ({textrm{GF}}(q)) is also a matrix of the same rank k over any extension field ({textrm{GF}}(q^ell )) and generates a linear code of the same length, same dimension and same minimum distance over ({textrm{GF}}(q^ell )), denoted by ({mathcal {C}}(q|q^ell )) and called a lifted code of ({mathcal {C}}). Although ({mathcal {C}}) and their lifted codes ({mathcal {C}}(q|q^ell )) have the same parameters, they have different weight distributions and different applications. Few results about lifted linear codes are known in the literature. This paper proves some fundamental theory for lifted linear codes, and studies the 2-designs of the lifted projective Reed–Muller codes, lifted Hamming codes and lifted Simplex codes. In addition, this paper settles the weight distributions of the lifted Reed–Muller codes of certain orders, and investigates the 3-designs supported by these lifted codes. As a by-product, an infinite family of three-weight projective codes over ({textrm{GF}}(4)) is obtained.","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"25 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2024-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142884413","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

Low-weight codewords in cyclic codes 循环码中的低权重码字

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-24 DOI: 10.1007/s10623-024-01547-y

J. G. Coelho, F. E. Brochero Martínez

引用次数: 0

A class of permutations on $${mathbb {Z}}_{p}$$ with differential uniformity at most 3 $${mathbb {Z}}_{p}$$上微分均匀性最多为3的一类置换

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-22 DOI: 10.1007/s10623-024-01548-x

Prachi Gupta, P. R. Mishra, Atul Gaur

引用次数: 0

Guessing less and better: improved attacks on GIFT-64 猜测更少，更好：改进对GIFT-64的攻击

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01527-2

Federico Canale, María Naya-Plasencia

引用次数: 0

On automorphism groups of binary cyclic codes 论二元循环码的自形群

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01539-y

Jicheng Ma, Guiying Yan

引用次数: 0

A construction of optimal quasi-cyclic locally recoverable codes using constituent codes 利用组成码构造最优拟循环局部可恢复码

IF 1.6 2区数学

Designs, Codes and Cryptography Pub Date : 2024-12-20 DOI: 10.1007/s10623-024-01532-5

Gustavo Terra Bastos, Angelynn Álvarez, Zachary Flores, Adriana Salerno

引用次数: 0

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