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Linear codes over finite fields parameterized by functions have proven to be a powerful tool in coding theory, yielding optimal and few-weight codes with significant applications in secret sharing, authentication codes, and association…

Information Theory · Computer Science 2026-02-17 Virginio Fratianni , Sihem Mesnager

Linear codes are the most important family of codes in cryptography and coding theory. Some codes have only a few weights and are widely used in many areas, such as authentication codes, secret sharing schemes and strongly regular graphs.…

Information Theory · Computer Science 2024-05-20 Shudi Yang , Tonghui Zhang , Zheng-An Yao

We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords…

Information Theory · Computer Science 2026-03-05 Antonio Jesús Lorite López , Daniel Camazón Portela , Juan Antonio López Ramos

Linear codes with a few weights can be applied to communication, consumer electronics and data storage system. In addition, the weight hierarchy of linear codes has many applications such as on the type II wire-tap channel, dealing with…

Information Theory · Computer Science 2021-06-08 Fei Li , Xiumei Li

Linear codes are widely studied in coding theory as they have nice applications in distributed storage, combinatorics, lattices, cryptography and so on. Constructing linear codes with desirable properties is an interesting research topic.…

Information Theory · Computer Science 2024-01-08 Ziling Heng , Xiaoru Li , Yansheng Wu , Qi Wang

Linear codes with a few weights are very important in coding theory and have attracted a lot of attention. In this paper, we present a construction of $q$-ary linear codes from trace and norm functions over finite fields. The weight…

Information Theory · Computer Science 2017-07-25 Ziling Heng , Qin Yue

Linear codes with few weights have been an interesting subject of study for many years, as these codes have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, linear codes…

Information Theory · Computer Science 2016-02-05 Chunming Tang , Can Xiang , Keqin Feng

Linear codes with a few weights can be applied to secrete sharing, authentication codes, association schemes and strongly regular graphs. For an odd prime power $q$, we construct a class of three-weight $\F_q$-linear codes from quadratic…

Information Theory · Computer Science 2024-10-04 Xiumei Li , Zongxi Chen , Fei Li

In this paper, we propose a class of linear codes and obtain their weight distribution. Some of these codes are almost optimal. Moreover, several classes of constant composition codes(CCCs) are constructed as subcodes of linear codes.

Information Theory · Computer Science 2017-06-28 Long Yu , Xiusheng Liu

Linear codes with a few weights are an important class of codes in coding theory and have attracted a lot of attention. In this paper, we present several constructions of $q$-ary linear codes with two or three weights from vectorial…

Information Theory · Computer Science 2022-07-26 Jiaxin Wang , Zexia Shi , Yadi Wei , Fang-Wei Fu

Linear codes with a few weights have many nice applications including combinatorial design, distributed storage system, secret sharing schemes and so on. In this paper, we construct two families of linear codes with a few weights based on…

Information Theory · Computer Science 2022-10-12 Ziling Heng , Xinran Wang , Xiaoru Li

Let $\mathbb{F}_{p^m}$ be a finite field with $p^m$ elements, where $p$ is an odd prime and $m$ is a positive integer. Recently, \cite{Hengar} and \cite{Wang2020} determined the weight distributions of subfield codes with the form…

Information Theory · Computer Science 2020-12-14 Dabin Zheng , Xiaoqiang Wang , Yayao Li , Mu Yuan

Due to their important applications to coding theory, cryptography, communications and statistics, combinatorial $t$-designs have been attracted lots of research interest for decades. The interplay between coding theory and $t$-designs has…

Combinatorics · Mathematics 2019-12-17 Rong Wang , Xiaoni Du , Cuiling Fan , Zhihua Niu

We contribute to the knowledge of linear codes from special polynomials and functions, which have been studied intensively in the past few years. Such codes have several applications in secret sharing, authentication codes, association…

Information Theory · Computer Science 2023-07-27 Virginio Fratianni

Studying the generalized Hamming weights of linear codes is a significant research area within coding theory, as it provides valuable structural information about the codes and plays a crucial role in determining their performance in…

Information Theory · Computer Science 2024-05-31 Wei Lu , Qingyao Wang , Xiaoqiang Wang , Dabin Zheng

Subfield codes of linear codes over finite fields have recently received much attention. Some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, the $q$-ary…

Information Theory · Computer Science 2023-03-08 Li Xu , Cuiling Fan , Sihem Mesnager , Rong Luo , Haode Yan

In this paper, based on the theory of defining sets, two classes of at most six-weight linear codes over $\mathbb{F}_p$ are constructed. The weight distributions of the linear codes are determined by means of Gaussian period and Weil sums.…

Information Theory · Computer Science 2024-12-19 Xina Zhang

We construct trace codes over $\Z_4$ by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new…

Information Theory · Computer Science 2017-07-04 Minjia Shi , Yan Liu , Randriam Hugues , Lin Sok , Patrick Sole

In this paper, based on the theory of defining sets, two classes of five-weight or six-weight linear codes over Fp are constructed. The weight distributions of the linear codes are determined by means of Weil sums and a new type of…

Information Theory · Computer Science 2021-04-09 Xina Zhang

In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings.…

Information Theory · Computer Science 2017-04-24 Xiusheng Liu , Hualu Liu