The minimum distance of the antiprimitive BCH code with designed distance 3

2025/05/07 by Xu, Haojie, Wu, Xia, Lu, Wei +1
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2505.04315

Abstract

Let C_{(q,q^m+1,3,h)} denote the antiprimitive BCH code with designed distance 3. In this paper, we demonstrate that the minimum distance d of C_{(q,q^m+1,3,h)} equals 3 if and only if gcd(2h+1,q+1,q^m+1)≠1. When both q and m are odd, we determine the sufficient and necessary condition for d=4 and fully characterize the minimum distance in this case. Based on these conditions, we investigate the parameters of C_{(q,q^m+1,3,h)} for certain h. Additionally, two infinite families of distance-optimal codes and several linear codes with the best known parameters are presented.

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