Two-weight codes and second order recurrences

2017/09/14 by Minjia Shi, Zhongyi Zhang, Shi, Minjia +4 · 1 citation
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) #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.1709.04585

10 pages

openalex publication_date 2017/09/14 · arxiv created 2017/09/16 · arxiv updated 2017/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Cyclic codes of dimension 2 over a finite field are shown to have at most two nonzero weights. This extends a construction of Rao et al (2010) and disproves a conjecture of Schmidt-White (2002). We compute their weight distribution, and give a condition on the roots of their check polynomials for them to be MDS.

Cited by

• The complete weight distribution of a family of irreducible cyclic codes of dimension two

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• The weight distributions of a class of cyclic codes II