Trace Codes with Few Weights over \mathbbF_p+u\mathbbF_p

2016/12/01 by Minjia Shi, Yan Liu, Shi, Minjia +3 · 1 citation
Computer Science · Engineering · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1612.00128

openalex publication_date 2016/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct an infinite family of two-Lee-weight and three-Lee-weight codes over the chain ring \mathbbF_p+u\mathbbF_p. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. Then by using a linear Gray map, we obtain an infinite family of abelian codes with few weights over \mathbbF_p. In particular, we obtain an infinite family of two-weight codes which meets the Griesmer bound with equality. Finally, an application to secret sharing schemes is given.

Cited by

• New few weight codes from trace codes over a local Ring

Related

• Two-weight and three-weight codes from trace codes over \mathbbF_p+u\mathbbF_p+v\mathbbF_p+uv\mathbbF_p
• Two-weight codes from trace codes over R_k
• Linear codes with few weights over \mathbbF₂+u\mathbbF₂
• New few weight codes from trace codes over a local Ring
• Two-Weight and a Few Weights Trace Codes over \mathbbF_q+u\mathbbF_q