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

Abstract

Let n1=df+1$n_{1}=df+1$ and n2=dfź+1$n_{2}=df^{\prime }+1$ be two distinct odd primes with positive integers d,f,fź$d, f, f^{\prime }$ and gcd(f,fź)=1$\gcd (f,f^{\prime })=1$. In this paper, we compute the linear complexity and the minimal polynomial of the two-prime Whiteman's generalized cyclotomic sequence of order d=6$d=6$ over GF(q)$\text {GF}(q)$, where q=pm$q=p^{m}$ and p is an odd prime and m is an integer. We employ this sequence of order 6 to construct several classes of cyclic codes over GF(q)$\text {GF}(q)$ with length n1n2$n_{1}n_{2}$. We also obtain lower bounds on the minimum distance of these cyclic codes.