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

Abstract. BinaryWhiteman’s cyclotomic sequences of orders 2 and 4 have a number of good randomness properties. In this paper, we compute the autocorrelation values and linear complexity of the first class two-prime Whiteman’s generalized cyclotomic sequence (WGCS-I) of order d = 6. Our results show that the autocorrelation values of this sequence is four-valued or five-valued if (n1−1)(n2−1)/36 is even or odd respectively, where n1 and n2 are two distinct odd primes and their linear complexity is quite good. We employ the two-prime WGCS-I of order 6 to construct several classes of cyclic codes over GF(q) with length n1n2. We also obtain the lower bounds on the minimum distance of these cyclic codes.