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The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. In this paper, we investigate the generalized Hamming weights of two classes of linear codes constructed from defining sets and determine them completely…

Information Theory · Computer Science 2019-05-08 Gaopeng Jian

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

The study of the generalized Hamming weight of linear codes is a significant research topic in coding theory as it conveys the structural information of the codes and determines their performance in various applications. However,…

Information Theory · Computer Science 2023-10-19 Chao Liu , Dabin Zheng , Wei Lu , Xiaoqiang Wang

The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…

Information Theory · Computer Science 2017-02-15 Gaopeng Jian

In this paper, we discuss the generalized Hamming weights of a class of linear codes associated with non-degenerate quadratic forms. In order to do so, we study the quadratic forms over subspaces of finite field and obtain some interesting…

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

The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we…

Information Theory · Computer Science 2015-04-07 Maosheng Xiong , Shuxing Li , Gennian Ge

In this work we develop a geometric approach to the study of rank metric codes. Using this method, we introduce a simpler definition for generalized rank weight of linear codes. We give a complete classification of constant rank weight code…

Information Theory · Computer Science 2020-01-23 Tovohery Hajatiana Randrianarisoa

The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one…

Information Theory · Computer Science 2022-12-08 Chao Liu , Dabin Zheng , Xiaoqiang Wang

Currently known secondary construction techniques for linear codes mainly include puncturing, shortening, and extending. In this paper, we propose a novel method for the secondary construction of linear codes based on their weight…

Information Theory · Computer Science 2025-11-25 Dongmei Huang , Qunying Liao , Sihem Mesnager , Gaohua Tang , Haode Yan

We use the relations between quadrics, trace codes and algebraic curves to construct algebraic curves over finite fields with many points and to compute generalized Hamming weights of codes.

alg-geom · Mathematics 2008-02-03 G. van der Geer , M. van der Vlugt

Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…

Information Theory · Computer Science 2017-11-15 Minglong Qi , Shengwu Xiong , Jingling Yuan , Wenbi Rao , Luo Zhong

In 1997 Rosenthal and York defined generalized Hamming weights for convolutional codes, by regarding a convolutional code as an infinite dimensional linear code endowed with the Hamming metric. In this paper, we propose a new definition of…

Information Theory · Computer Science 2022-07-26 Elisa Gorla , Flavio Salizzoni

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper we elaborate on the implication of these parameters and we devise a method to estimate…

Information Theory · Computer Science 2015-02-04 Olav Geil , Stefano Martin , Ryutaroh Matsumoto , Diego Ruano , Yuan Luo

The aim of this work is to algebraically describe the relative generalized Hamming weights of evaluation codes. We give a lower bound for these weights in terms of a footprint bound. We prove that this bound can be sharp. We compute the…

Information Theory · Computer Science 2024-02-07 Delio Jaramillo-Velez , Hiram H. López , Yuriko Pitones

The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of…

Commutative Algebra · Mathematics 2020-05-20 Delio Jaramillo , Maria Vaz Pinto , Rafael H. Villarreal

In this paper we find the second generalized Hamming weight of some evaluation codes arising from a projective torus, and it allows to compute the second generalized Hamming weight of the codes parameterized by the edges of any complete…

Information Theory · Computer Science 2018-10-22 Manuel González Sarabia , Eduardo Camps , Eliseo Sarmiento , Rafael H. Villarreal

The determination of weight distribution of cyclic codes involves evaluation of Gauss sums and exponential sums. Despite of some cases where a neat expression is available, the computation is generally rather complicated. In this note, we…

Information Theory · Computer Science 2017-03-21 Shuxing Li , Sihuang Hu , Tao Feng , Gennian Ge

The generalized Hamming weights (GHWs) are fundamental parameters of linear codes. GHWs are of great interest in many applications since they convey detailed information of linear codes. In this paper, we continue the work of [10] to study…

Information Theory · Computer Science 2017-02-07 Shuxing Li

We construct a class of linear codes by choosing a proper defining set and determine their complete weight enumerators and weight enumerators. The results show that they are at most three-weight codes and they are suitable for applications…

Information Theory · Computer Science 2019-01-23 Shudi Yang , Xiangli Kong

We study the generalized rank weight distribution of a linear code. First, we provide a MacWilliams-type identity which relates the distributions of a code and its dual. Then, we give a formula for the enumerator polynomial. Finally, we…

Information Theory · Computer Science 2026-02-12 Julien Molina
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