Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6

Bull. Korean Math. Soc. Published online 2019 Mar 11

Pramo Kumar Kewat, and Priti Kumari
Indian Institute of Technology(Indian School of Mines), Dhanbad

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.