Abstract
Let \(n_{1}=df+1\) and \(n_{2}=df^{\prime }+1\) be two distinct odd primes with positive integers \(d,\ f,\ f^{\prime }\) and \(\gcd (f,f^{\prime })=1\). In this paper, we compute the linear complexity and the minimal polynomial of the two-prime Whiteman’s generalized cyclotomic sequence of order \(d=6\) over \(\text {GF}(q)\), where \(q=p^{m}\) 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 \(\text {GF}(q)\) with length \(n_{1}n_{2}\). We also obtain lower bounds on the minimum distance of these cyclic codes.
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Kewat, P.K., Kumari, P. Cyclic codes from the second class two-prime Whiteman’s generalized cyclotomic sequence with order 6. Cryptogr. Commun. 9, 475–499 (2017). https://doi.org/10.1007/s12095-016-0191-8
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DOI: https://doi.org/10.1007/s12095-016-0191-8