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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

Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $\ell_1$-metric. By using packings and group divisible designs in combinatorial design theory, we give…

Information Theory · Computer Science 2020-10-12 Tingting Chen , Yiming Ma , Xiande Zhang

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear…

Information Theory · Computer Science 2015-04-15 Markus Grassl , Peter Shor , Graeme Smith , John Smolin , Bei Zeng

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

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group $(\gf(2^{2m}), +)$, have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective…

Combinatorics · Mathematics 2019-04-26 Cunsheng Ding , Akihiro Munemasa , Vladimir Tonchev

The linear codes with a few weights have been applied widely in combinatorial designs, secret sharing, association schemes, authentication codes and strongly regular graphs. In this paper, we first correct an erroneous result about the…

Information Theory · Computer Science 2020-09-21 Fei Li , Xiumei Li

We study the performance of ternary isodual codes which are not self-dual and ternary self-dual codes, as measured by the decoding error probability in bounded distance decoding. We compare the performance of ternary double circulant and…

Information Theory · Computer Science 2016-09-08 T. Aaron Gulliver , Masaaki Harada

We construct strongly walk-regular graphs as coset graphs of the duals of codes with three non-zero homogeneous weights over $\mathbb{Z}_{p^m},$ for $p$ a prime, and more generally over chain rings of depth $m$, and with a residue field of…

Combinatorics · Mathematics 2019-12-10 Michael Kiermaier , Sascha Kurz , Minjia Shi , Patrick Solé

We give two methods for constructing many linear complementary dual (LCD for short) codes from a given LCD code, by modifying some known methods for constructing self-dual codes. Using the methods, we construct binary LCD codes and…

Information Theory · Computer Science 2021-01-29 Masaaki Harada

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

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

In the past few years, linear codes with few weights and their weight analysis have been widely studied. In this paper, we further investigate a class of two-weight or three-weight linear codes from defining sets and determine their weight…

Information Theory · Computer Science 2020-09-11 Dabin Zheng , Qing Zhao , Xiaoqiang Wang , Yan Zhang

In this article we mainly study linear codes over $\mathbb{F}_{2^n}$ and their binary subfield codes. We construct linear codes over $\mathbb{F}_{2^n}$ whose defining sets are the certain subsets of $\mathbb{F}_{2^n}^m$ obtained from…

Information Theory · Computer Science 2023-03-17 Hongwei Liu , Zihao Yu

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Computer Vision and Pattern Recognition · Computer Science 2018-12-26 Konstantinos Makantasis , Anastasios Doulamis , Nikolaos Doulamis , Antonis Nikitakis

As a subclass of linear codes, cyclic codes have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, five families of three-weight…

Information Theory · Computer Science 2013-08-27 Cunsheng Ding , Ying Gao , Zhengchun Zhou

In this paper, for an odd prime $p$, by extending Li et al.'s construction \cite{CL2016}, several classes of two-weight and three-weight linear codes over the finite field $\mathbb{F}_p$ are constructed from a defining set, and then their…

Information Theory · Computer Science 2021-07-07 Canze Zhu , Qunying Liao

Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…

Information Theory · Computer Science 2020-07-23 Guangkui Xu , Xiwang Cao

In this article a technique for constructing $p$-ary bent functions from near-bent functions is presented. Two classes of quadratic $p$-ary functions are shown to be near-bent. Applying the construction of bent functions to these classes of…

Combinatorics · Mathematics 2010-11-30 Ayca Cesmelioglu , Gary McGuire , Wilfried Meidl

It has been known for a long time that $t$-designs can be employed to construct both linear and nonlinear codes and that the codewords of a fixed weight in a code may hold a $t$-design. While a lot of progress in the direction of…

Information Theory · Computer Science 2017-06-02 Cunsheng Ding

In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and…

Cryptography and Security · Computer Science 2012-11-20 Fengrong Zhang , Claude Carlet , Yupu Hu , Wenzheng Zhang