Two-weight codes from trace codes over R_k

2016/12/16 by Minjia Shi, Shi, Minjia, Yue Guan +1
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.1612.05523

openalex publication_date 2016/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a family of two-Lee-weight codes over the ring R_k, which is defined as trace codes with algebraic structure of abelian codes. The Lee weight distribution of the two-weight codes is given. Taking the Gray map, we obtain optimal abelian binary two-weight codes by using the Griesmer bound. An application to secret sharing schemes is also given.

Related

• Two-weight and three-weight codes from trace codes over \mathbbF_p+u\mathbbF_p+v\mathbbF_p+uv\mathbbF_p
• Trace Codes with Few Weights over \mathbbF_p+u\mathbbF_p
• 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