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We consider linear codes over a finite field of odd characteristic, derived from determinantal varieties, obtained from symmetric matrices of bounded ranks. A formula for the weight of a code word is derived. Using this formula, we have…

Information Theory · Computer Science 2023-12-25 Peter Beelen , Trygve Johnsen , Prasant Singh

The interplay between coding theory and $t$-designs has attracted a lot of attention for both directions. It is well known that the supports of all codewords with a fixed weight in a code may hold a $t$-design. In this paper, by determining…

Combinatorics · Mathematics 2019-03-19 Xiaoni Du , Rong Wang , Chunming Tang , Qi Wang

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

Linear codes with few weights have applications in secrete sharing, authentication codes, association schemes, and strongly regular graphs. In this paper, several classes of $p$-ary linear codes with two or three weights are constructed…

Information Theory · Computer Science 2015-10-20 Zhengchun Zhou , Nian Li , Cuiling Fan , Tor Helleseth

The sizes of optimal constant-composition codes of weight three have been determined by Chee, Ge and Ling with four cases in doubt. Group divisible codes played an important role in their constructions. In this paper, we study the problem…

Information Theory · Computer Science 2015-03-13 Mingzhi Zhu , Gennian Ge

In this article we present a class of codes with few weights arising from special type of linear sets. We explicitly show the weights of such codes, their weight enumerator and possible choices for their generator matrices. In particular,…

Combinatorics · Mathematics 2020-05-07 Vito Napolitano , Ferdinando Zullo

We show an interesting PBD-closure result for the set of lengths of constant-composition codes whose distance and size meet certain conditions. A consequence of this PBD-closure result is that the size of optimal constant-composition codes…

Information Theory · Computer Science 2007-12-18 Yeow Meng Chee , Alan C. H. Ling , San Ling , Hao Shen

Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…

Rings and Algebras · Mathematics 2018-04-04 Ted Hurley

This paper provides new constructive lower bounds for constant dimension codes, using different techniques such as Ferrers diagram rank metric codes and pending blocks. Constructions for two families of parameters of constant dimension…

Information Theory · Computer Science 2014-09-03 Natalia Silberstein , Anna-Lena Trautmann

Multiply constant-weight codes (MCWCs) have been recently studied to improve the reliability of certain physically unclonable function response. In this paper, we give combinatorial constructions for MCWCs which yield several new infinite…

Information Theory · Computer Science 2014-11-11 Yeow Meng Chee , Han Mao Kiah , Hui Zhang , Xiande Zhang

Constant dimension codes are e.g. used for error correction and detection in random linear network coding, so that constructions for these codes have achieved wide attention. Here, we improve over 150 lower bounds by describing better…

Information Theory · Computer Science 2020-04-30 Sascha Kurz

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

We will show how to obtain a linear code from a configuration of affine lines in general position and a suitable set of rational points. We will also explain a new decoding algorithm based on the configuration, which seems to be quite…

Information Theory · Computer Science 2007-08-22 Ken-ichi Sugiyama

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

For the past decades, linear codes with few weights have been widely studied, since they have applications in space communications, data storage and cryptography. In this paper, a class of binary linear codes is constructed and their weight…

Information Theory · Computer Science 2016-02-03 Fei Li , Yang Yan , Qiuyan Wang , Tongjiang Yan

In this paper, we present a construction of linear codes over $\f_{2^t}$ from Boolean functions, which is a generalization of Ding's method \cite[Theorem 9]{Ding15}. Based on this construction, we give two classes of linear codes…

Information Theory · Computer Science 2015-11-10 Can Xiang , Keqin Feng , Chunming Tang

Firstly, we give a formula on the generalized Hamming weight of linear codes constructed generically by defining sets. Secondly, by choosing properly the defining set we obtain a class of cyclotomic linear codes and then present two…

Information Theory · Computer Science 2022-06-17 Fei Li

This paper introduces a new combinatorial construction for q-ary constant-weight codes which yields several families of optimal codes and asymptotically optimal codes. The construction reveals intimate connection between q-ary…

Information Theory · Computer Science 2007-07-13 Yeow Meng Chee , San Ling

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

Linearized Reed-Solomon codes are defined. Higher weight distribution of those codes are determined.

Information Theory · Computer Science 2015-05-28 Haode Yan , Yan Liu , Chunlei Liu