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Cyclic codes from the first class two-prime Whiteman's generalized cyclotomic sequence with order 6
Pramod Kumar Kewat,Priti Kumari 대한수학회 2019 대한수학회보 Vol.56 No.2
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.
CYCLIC CODES FROM THE FIRST CLASS TWO-PRIME WHITEMAN'S GENERALIZED CYCLOTOMIC SEQUENCE WITH ORDER 6
Kewat, Pramod Kumar,Kumari, Priti Korean Mathematical Society 2019 대한수학회보 Vol.56 No.2
Let $p_1$ and $p_2$ be two distinct odd primes with 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 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.