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Weight Distributions of Two Classes of Cyclic Codes With Respect to Two Distinct Order Elements

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2 Author(s)
Chengju Li ; Math. Dept., Nanjing Univ. of Aeronaut. & Astronaut., Nanjing, China ; Qin Yue

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 distributions are known only for a few cases. In this paper, let Fr be an extension of a finite field Fq and r = qm, we determine the weight distributions of the cyclic codes C={c(a, b): a, b ∈ Fr}, c(a, b)= Trr/q(ag10 +bg20),...,Trr/q(ag1n-1+bg2n-1)), g1, g2 ∈ Fr, in the following two cases: 1) ord(g1)=n, n|r-1 and g2=1 and 2) ord(g1)=n, g2=g12, ord(g2)=n/2, m=2, and 2(r-1)/n|(q+1).

Published in:

IEEE Transactions on Information Theory  (Volume:60 ,  Issue: 1 )