检索结果-内蒙古大学图书馆

A family of linear codes with few weights and their subfield codes

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2025年第1期17卷 207-238页

作者： Ding, Yun Zhu, Shixin Hefei Univ Technol Sch Math Hefei Peoples R China

Linear codes with few weights have many applications in secret sharing, strongly regular graphs, association schemes and authentication codes. Recently, subfield codes of some linear codes with few weights have been studied. In this paper, we present a family of linear codes with few weights and their punctured codes, whose parameters and weight distributions are completely determined. And we give the parameters of their dual codes, which are length-optimal and dimensional-optimal with respect to the Sphere-packing bound. In addition, we also investigate their subfield codes to obtain some q-ary linear codes with few weights. The weight distributions and dualities of these subfield codes are explicitly determined.

关键词： Linear code subfield code Weight distribution Few-weight code

来源：评论

学校读者我要写书评

暂无评论

subfield codes of CD-codes over F2[x]/⟨x³ - x⟩

引用

DISCRETE MATHEMATICS 2025年第1期348卷

作者： Bhagat, Anuj Kumar Sarma, Ritumoni Sagar, Vidya Indian Inst Technol Delhi Dept Math New Delhi 110016 India

A non-zero F-linear map from a finite-dimensional commutative F-algebra to the field Fis called an F-valued trace if its kernel does not contain any non-zero ideals. In this article, we utilize an F2-valued trace of the F2-algebra R2:= F2[x]/x3- x to study binary subfield code C(2) Dof CD:={(x center dot d) d.D: x. Rm2} for each defining set Dderived from a certain simplicial complex. For m. Nand X.{1, 2,..., m}, define X:={v. Fm2: Supp(v). X} and D :=(1 + u2) D1+ u2D2+(u + u2)D3, a subset of Rm2, where u = x + x3- x, D1.{L, cL}, D2.{ M, cM} and D3.{N, cN}, for L, M, N.{1, 2,..., m}. The parameters and the Hamming weight distribution of the binary subfield code C(2)Dof CDare determined for each D. These binary subfield codes are minimal under certain mild conditions on the cardinalities of L, Mand N. Moreover, most of these codes are distanceoptimal. Consequently, we obtain a few infinite families of minimal, self-orthogonal and distance-optimal binary linear codes that are either 2-weight or 4-weight. It is worth mentioning that we have obtained several new distance-optimal binary linear codes. (c) 2024 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

关键词： Linear code subfield code Minimal code Optimal code Self-orthogonal code Simplicial complex

来源：评论

学校读者我要写书评

暂无评论

subfield codes of Several Few-Weight Linear codes Parameterized by Functions and Their Consequences

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2024年第6期70卷 3941-3964页

作者： Xu, Li Fan, Cuiling Mesnager, Sihem Luo, Rong Yan, Haode Southwest Jiaotong Univ Sch Math Chengdu 610031 Peoples R China Univ Paris VIII Dept Math F-93526 St Denis France Univ Paris XIII CNRS UMR LAGA 7539 F-93430 Villetaneuse France Polytech Inst Paris Telecom Paris F-91120 Palaiseau France

subfield codes of linear codes over finite fields have recently received much attention since they can produce optimal codes, which may have applications in secret sharing, authentication codes and association schemes. In this paper, we first present a construction framework of 3-dimensional linear codes C(f.g )over F-q(m) parameterized by any two functions f, g over F-q(m) , and then study the properties of six types of C-f.g, its punctured code C-f.g*, and their corresponding subfield codes over F-q. The classification of C-f,C-g is based on special choices of f, g as trace function, norm function, almost bent function, Boolean bent function or a combination of these functions. For the first two types of C-f.g, we explicitly determine the weight distributions and dualities of C-f,C-g, C-f.g* and their subfield codes over F-q. The remaining four types of C-f.g are restricted to q = 2, and the weight distributions and dualities of the subfields code C-f,C-g(q) and C-f.g(*(q)) are completely determined. Most of the resultant linear codes (over F-q(m) or over F-q) have few weights. Some of them are optimal and some have the best-known parameters according to the tables maintained at http://***. In fact, 16 infinite families of optimal linear codes are produced in this paper. As a byproduct, a family of [2(4m-2), 2m+1, 2(4m-3)] quaternary Hermitian self-orthogonal codes are obtained with m >= 2. As an application, we present several infinite families of 2-designs or 3-designs with some of the codes presented in this paper.

关键词： codes Linear codes codecs Generators Fans Cryptography Transforms Linear code subfield code weight distribution few-weight code (almost) bent function design

来源：评论

学校读者我要写书评

暂无评论

On four conjectures of Heng-Ding and p-ary linear codes from monomials

引用

IEEE Transactions on Information Theory 2025年

作者： Qian, Liqin Shi, Minjia Anhui University School of Mathematical Sciences Anhui Hefei230601 China Anhui University Key Laboratory of Intelligent Computing Signal Processing Ministry of Education School of Mathematical Sciences Anhui Hefei230601 China Xidian University State Key Laboratory of Integrated Service Networks Xi'an710071 China

subfield codes of linear codes over finite fields have recently attracted great attention due to their wide applications in secret sharing schemes, authentication codes and association schemes. There are two major ingredients in this paper. The first ingredient is to solve four conjectures recently proposed by Heng and Ding (IEEE Trans. Inf. Theory, 68(6): 3643-3656, 2022). Besides, we also determine the weight distributions of subfield codes derived from x3 and oval polynomials over F2m. The second ingredient is to obtain two classes of p-ary linear codes from monomials over Fpm. We study the parameters of the constructed codes and determine their weight distributions. Notably, we show that the codes C(p) (xpi, pm) are optimal and almost optimal in many cases with respect to the online Database of Grassl. Finally, we observe that the derived linear codes also have the minimality property for most cases. © 1963-2012 IEEE.

关键词： Linear code monomial oval polynomial subfield code weight distribution

来源：评论

学校读者我要写书评

暂无评论

The subfield codes of hyperoval and conic codes

引用

FINITE FIELDS AND THEIR APPLICATIONS 2019年 56卷 308-331页

作者： Heng, Ziling Ding, Cunsheng Changan Univ Sch Sci Xian 710064 Shaanxi Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Kowloon Clear Water Bay Hong Kong Peoples R China

Hyperovals in PG(2, GF(q)) with even q are maximal arcs and an interesting research topic in finite geometries and combinatorics. Hyperovals in PG(2, GF(q)) are equivalent to [q + 2, 3, q] MDS codes over GF(q), called hyperoval codes, in the sense that one can be constructed from the other. Ovals in PG(2, GF(q)) for odd q are equivalent to [q + 1, 3, q - 1] MDS codes over GF(q), which are called oval codes. In this paper, we investigate the binary subfield codes of two families of hyperoval codes and the p-ary subfield codes of the conic codes. The weight distributions of these subfield codes and the parameters of their duals are determined. As a byproduct, we generalize one family of the binary subfield codes to the p-ary case and obtain its weight distribution. The codes presented in this paper are optimal or almost optimal in many cases. In addition, the parameters of these binary codes and p-ary codes seem new. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Oval Hyperoval Conic Linear code subfield code

来源：评论

学校读者我要写书评

暂无评论

Two families of subfield codes with a few weights

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2021年第1期13卷 117-127页

作者： Xiang, Can Yin, Wenjuan South China Agr Univ Coll Math & Informat Guangzhou 510642 Guangdong Peoples R China Nankai Univ Chern Inst Math Tianjin 300071 Peoples R China Nankai Univ LPMC Tianjin 300071 Peoples R China

subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, two families of binary subfield codes with a few weights are presented from two special classes of linear codes, and their parameters are explicitly determined. Moreover, the parameters of the duals of these subfield codes are also studied. The two infinite families of subfield codes presented in this paper are distance-optimal with respect to the Griesmer bound and their duals are almost distance-optimal with respect to the sphere-packing bound.

关键词： Linear code subfield code Distance-optimal

来源：评论

学校读者我要写书评

暂无评论

The subfield codes of several classes of linear codes

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2020年第6期12卷 1111-1131页

作者： Wang, Xiaoqiang Zheng, Dabin Hubei Univ Fac Math & Stat Hubei Key Lab Appl Math Wuhan 430062 Peoples R China

Let F-2m be the finite field with 2(m) elements, where m is a positive integer. Recently, Heng and Ding in (Finite Fields Appl. 56:308-331, 2019) studied the subfield codes of two families of hyperovel codes and determined the weight distribution of the linear code C-a,C-b = {((Tr-1(m) (af (x) + bx) + c)(x is an element of F2m), Tr-1(m) (a), Tr-1(m) (b)) : a, b is an element of F-2m, c is an element of F-2}, for f (x) = x(2) and f (x) = x(6) with odd m. Let v(2)(.) denote the 2-adic order function. This paper investigates more subfield codes of linear codes and obtains the weight distribution of C-a,C-b for f (x) = x(2i+2j), where i, j are nonnegative integers such that v(2)(m) <= v(2)(i - j) (i >= j). In addition to this, we further investigate the punctured code of C-a,C-b as follows: C-a = {((Tr-1(m)(ax(2i+2j) + bx) + c)(x is an element of F2m), Tr-1(m)(a)) : a, b is an element of F-2m, c is an element of F-2}, and determine its weight distribution for any nonnegative integers i, j. The parameters of these binary linear codes are new in most cases. Some of the codes and their duals obtained are optimal or almost optimal.

关键词： Weight distribution subfield code Linear code Optimal code

来源：评论

学校读者我要写书评

暂无评论

Quaternary Linear codes and Related Binary subfield codes

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第5期68卷 3070-3080页

作者： Wu, Yansheng Li, Chengju Xiao, Fu Nanjing Univ Posts & Telecommun Sch Comp Sci Nanjing 210023 Peoples R China East China Normal Univ Shanghai Key Lab Trustworthy Comp Shanghai 200062 Peoples R China

In this paper, we mainly study quaternary linear codes and their binary subfield codes. First we obtain a general explicit relationship between quaternary linear codes and their binary subfield codes in terms of generator matrices and defining sets. Second, we construct quaternary linear codes via simplicial complexes and determine the weight distributions of these codes. Third, the weight distributions of the binary subfield codes of these quaternary codes are also computed by employing the general characterization. Furthermore, we present two infinite families of optimal linear codes with respect to the Griesmer Bound, and a class of binary almost optimal codes with respect to the Sphere Packing Bound. We also need to emphasize that we obtain at least 9 new quaternary linear codes.

关键词： codes Linear codes codecs Generators Telecommunications Computer science Technological innovation Quaternary linear code subfield code weight distribution simplicial complex

来源：评论

学校读者我要写书评

暂无评论

Several classes of linear codes with AMDS duals and their subfield codes

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES 2024年第6期16卷 1429-1448页

作者： Qiao, Xingbin Du, Xiaoni Yuan, Wenping Northwest Normal Univ Coll Math & Stat Lanzhou 730070 Peoples R China Northwest Normal Univ Key Lab Cryptog & Data Analyt Lanzhou 730070 Peoples R China Gansu Prov Res Ctr Basic Disciplines Math & Stat Lanzhou 730070 Peoples R China

subfield codes of linear codes over finite fields have recently attracted great attention due to their wide applications in secret sharing, authentication codes and association schemes. In this paper, we first present a construction of 3-dimensional linear codes C-f over finite field F-2(m) parameterized by any Boolean function f. Then we determine explicitly the weight distributions of C-f, the punctured code (C) over tilde (f), as well as the corresponding subfield codes over F-2 for several classes of Boolean functions ff. In particular, we determine the weight distributions of subfield codes derived from r-plateaued functions. Moreover, the parameters of their dual codes are investigated, which contain length-optimal and dimension-optimal AMDS codes with respect to the sphere packing bound. We emphasize that the new codes are projective and contain binary self-complementary codes. As applications, some of the projective codes we present can be employed to construct s-sum sets for any odd integer s >1.

关键词： Linear code Punctured code subfield code Projective code Weight distribution

来源：评论

学校读者我要写书评

暂无评论

The subfield codes and subfield Subcodes of a Family of MDS codes

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2022年第9期68卷 5792-5801页

作者： Tang, Chunming Wang, Qi Ding, Cunsheng China West Normal Univ Sch Math & Informat Nanchong 637002 Peoples R China Southern Univ Sci & Technol Natl Ctr Appl Math Shenzhen Shenzhen 518055 Peoples R China Southern Univ Sci & Technol Dept Comp Sci & Engn Shenzhen 518055 Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Peoples R China

Maximum distance separable (MDS) codes are very important in both theory and practice. There is a classical construction of a family of [2(m) +1, 2u -1, 2(m) - 2u + 3] MDS codes for 1 <= u <= 2(m)(-1), which are cyclic, reversible and BCH codes over GF(2(m)). The objective of this paper is to study the quaternary subfield subcodes and quaternary subfield codes of a subfamily of the MDS codes for even m. A family of quaternary cyclic codes is obtained. These quaternary codes are distance-optimal in some cases and very good in general. Furthermore, two infinite families of 3-designs from these quaternary codes and their duals are presented.

关键词： BCH code cyclic code MDS code subfield code subfield subcode t-design

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：