Linear Codes over \mathbbF_q[x]/(x²) and GR(p²,m) Reaching the Griesmer Bound

2016/12/04 by Jin Li, Aixian Zhang, Li, Jin +3
Computer Science · Mathematics · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1612.01096

openalex publication_date 2016/12/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct two series of linear codes over finite ring \mathbbF_q[x]/(x²) and Galois ring GR(p²,m) respectively reaching the Griesmer bound. They derive two series of codes over finite field \mathbbF_q by Gray map. The first series of codes over \mathbbF_q derived from \mathbbF_q[x]/(x²) are linear and also reach the Griesmer bound in some cases. Many of linear codes over finite field we constructed have two Hamming (non-zero) weights.

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