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Recently, the weight distributions of the duals of the cyclic codes with two zeros have been obtained for several cases. In this paper we solve one more special case. The problem of finding the weight distribution is transformed into a…

Number Theory · Mathematics 2012-10-17 Maosheng Xiong

In this manuscript, we construct a class of projective three-weight linear codes and two classes of projective four-weight linear codes over F2 from the defining sets construction, and determine their weight distributions by using additive…

Information Theory · Computer Science 2025-11-04 Qunying Liao , Zhaohui Zhang , Peipei Zheng

In this paper, we present the harmonic generalizations of well-known polynomials of codes over finite fields, namely the higher weight enumerators and the extended weight enumerators, and we derive the correspondences between these weight…

Combinatorics · Mathematics 2025-06-16 Thomas Britz , Himadri Shekhar Chakraborty , Tsuyoshi Miezaki

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

A class of optimal three-weight cyclic codes of dimension 3 over any finite field was presented by Vega [Finite Fields Appl., 42 (2016) 23-38]. Shortly thereafter, Heng and Yue [IEEE Trans. Inf. Theory, 62(8) (2016) 4501-4513] generalized…

Information Theory · Computer Science 2021-07-12 Gerardo Vega , Félix Hernández

In the present paper we introduce and study finite point subsets of a special kind, called optimum distributions, in the n-dimensional unit cube. Such distributions are closely related with known (delta,s,n)-nets of low discrepancy. It…

Combinatorics · Mathematics 2007-07-16 M. M. Skriganov

Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…

Information Theory · Computer Science 2020-06-18 Xiaoqiang Wang , Dabin Zheng , Yan Zhang

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…

Information Theory · Computer Science 2017-03-21 Minjia Shi , Rongsheng Wu , Liqin Qian , Lin Sok , Patrick Solé

In this paper, several classes of three-weight codes and two-weight codes for the homogeneous metric over the chain ring $R=\mathbb{F}_p+u\mathbb{F}_p+\cdots +u^{k-1}\mathbb{F}_{p},$ with $u^k=0,$ are constructed, which generalises…

Information Theory · Computer Science 2017-01-10 Minjia Shi , Rongsheng Wu , Liqin Qian , Lin Sok , Patrick Sole

The duals of cyclic codes with two zeros have been extensively studied, and their weight distributions have recently been evaluated in some cases. In this note, we determine the weight distribution of a certain new class of such codes by…

Combinatorics · Mathematics 2012-06-18 Tao Feng , Koji Momihara

Recently, some infinite families of binary minimal and optimal linear codes are constructed from simplicial complexes by Hyun {\em et al}. Inspired by their work, we present two new constructions of codes over the ring $\Bbb F_2+u\Bbb F_2$…

Information Theory · Computer Science 2019-10-11 Yansheng Wu , Xiaomeng Zhu , Qin Yue

Cyclic codes have attracted a lot of research interest for decades. In this paper, for an odd prime $p$, we propose a general strategy to compute the complete weight enumerator of cyclic codes via the value distribution of the corresponding…

Information Theory · Computer Science 2016-03-01 Shudi Yang , Zheng-An Yao

One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…

Information Theory · Computer Science 2025-11-25 Usman Mushrraf , Ferdinando Zullo

Linear codes with few weights have significant applications in secret sharing schemes, authentication codes, association schemes, and strongly regular graphs. There are a number of methods to construct linear codes, one of which is based on…

Information Theory · Computer Science 2023-11-01 Yadi Wei , Jiaxin Wang , Fang-Wei Fu

In the recent work \cite{shi18}, a combinatorial problem concerning linear codes over a finite field $\F_q$ was introduced. In that work the authors studied the weight set of an $[n,k]_q$ linear code, that is the set of non-zero distinct…

Information Theory · Computer Science 2022-07-18 Tim L. Alderson , Alessandro Neri

Linear codes with few weights have many applications in secret sharing schemes, authentication codes, communication and strongly regular graphs. In this paper, we consider linear codes with three weights in arbitrary characteristic. To do…

Information Theory · Computer Science 2017-03-27 Sihem Mesnager , Ferruh Özbudak , Ahmet Sınak

Few-weight codes have been constructed and studied for many years, since their fascinating relations to finite geometries, strongly regular graphs and Boolean functions. Simplex codes are one-weight Griesmer $[\frac{q^k-1}{q-1},k…

Information Theory · Computer Science 2024-08-20 Xu Pan , Hao Chen , Hongwei Liu , Shengwei Liu

We consider the weight spectrum of a class of quasi-perfect binary linear codes with code distance 4. For example, extended Hamming code and Panchenko code are the known members of this class. Also, it is known that in many cases Panchenko…

Information Theory · Computer Science 2017-06-13 Valentine B. Afanassiev , Alexander A. Davydov

We express the weight enumerators of self-dual and doubly even (Type II for short) codes of length $24$ with a specified basis. As a consequence, we present some congruence relations among the weight enumerators.

Combinatorics · Mathematics 2023-03-15 Shoyu Nagaoka , Manabu Oura

In this work, we determine new linear equations for the weight distribution of linear codes over finite chain rings. The identities are determined by counting the number of some special submatrices of the parity-check matrix of the code.…

Information Theory · Computer Science 2022-10-31 Giulia Cavicchioni , Alessio Meneghetti
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