Two new families of linear codes with five Lee-weights over Fq+uFq and their Gray images

Linear codes with few weights have many applications in secret sharing, strongly regular graphs and association schemes. In this paper, by taking proper defining sets, we first present two new infinite families of linear codes with five Lee-weights over Fq+uFq and exactly determine the complete weig...

Full description

Saved in:
Bibliographic Details
Published inDiscrete mathematics Vol. 348; no. 12
Main Authors Ding, Yun, Zhu, Shixin
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2025
Subjects
Complete weight enumerator
Lee-weight distribution
Linear code
Minimal linear code
Linear code
Lee-weight distribution
Complete weight enumerator
Minimal linear code
Online AccessGet full text

Cover

More Information
Summary:Linear codes with few weights have many applications in secret sharing, strongly regular graphs and association schemes. In this paper, by taking proper defining sets, we first present two new infinite families of linear codes with five Lee-weights over Fq+uFq and exactly determine the complete weight enumerators of their Gray images. As an application, we also show that Gray images of the two families of linear codes are two new infinite families of minimal linear codes with wminwmax<q−1q, where wmin and wmax denote the minimum and maximum nonzero weights in the code, respectively.
ISSN:0012-365X
DOI:10.1016/j.disc.2025.114643