Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6
Bull. Korean Math. Soc. 2019 Vol. 56, No. 2, 285-301
https://doi.org/10.4134/BKMS.b170594
Published online March 1, 2019
Pramod Kumar Kewat, Priti Kumari
Indian Institute of Technology (Indian School of Mines); Indian Institute of Technology (Indian School of Mines)
Abstract : Let $p_1$ and $p_2$ be two distinct odd primes with $\mathrm{gcd}(p_1-1,p_2-1)=6$. In this paper, we compute the linear complexity of the first class two-prime Whiteman's generalized cyclotomic sequence (WGCS-I) of order $d=6$. Our results show that their linear complexity is quite good. So, the sequence can be used in many domains such as cryptography and coding theory. This article enrich a method to construct several classes of cyclic codes over $\mathrm{GF}(q)$ with length $n=p_1p_2$ using the two-prime WGCS-I of order 6. We also obtain the lower bounds on the minimum distance of these cyclic codes.
Keywords : cyclic codes, finite fields, cyclotomic sequences
MSC numbers : 94A05, 94A55, 94B15
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