Weight distribution of two classes of cyclic codes with respect to two distinct order elements

2013/06/22 by Chengju Li, Qin Yue, Li, Chengju +1 · 1 citation
Computer Science · Mathematics · #11T24 #11T71 #94B15 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT) #cs.IT #math.IT #math.NT #msc:11T24 #msc:11T71 #msc:94B15

paper · pdf · doi:10.48550/arxiv.1306.5277

arxiv created 2013/06/22 · arxiv updated 2013/06/25

Abstract

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Cyclic codes have been studied for many years, but their weight distribution are known only for a few cases. In this paper, let \Bbb F_r be an extension of a finite field \Bbb F_q and r=q^m, we determine the weight distribution of the cyclic codes \mathcal C=\c(a, b): a, b ∈ \Bbb F_r\, c(a, b)=(\mbox Tr_r/q(ag₁⁰+bg₂⁰), …, \mbox Tr_r/q(ag₁^n-1+bg₂^n-1)), g₁, g₂∈ \Bbb F_r, in the following two cases: (1) \ord(g₁)=n, n|r-1 and g₂=1; (2) \ord(g₁)=n, g₂=g₁², \ord(g₂)=\frac n 2, m=2 and \frac2(r-1)n|(q+1).

Cited by

• Weight distributions of cyclic codes with respect to pairwise coprime order elements

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