Linear Complexity of d-Ary Sequence Derived from Euler Quotients over GF(q)

For an odd prime p and positive integers r, d such that 0 < d ≤ p^r, a generic construction of dary sequence based on Euler quotients is presented in this paper. Compared with the known construction, in which the support set of the sequence is fixed and d is usually required to be a prime, the support set of the proposed sequence is flexible and d could be any positive integer less then p^r in our construction. Furthermore, the linear complexity of the proposed sequence over prime field GF(q) with the assumption of q^p-1 ≢ 1 mod p² is determined. An algorithm of computing the linear complexity of the sequence is also given. Our results indicate that, with some constrains on the support set, the new sequences possess large linear complexities.