Linear Complexity of <i>d</i> ‐Ary Sequence Derived from Euler Quotients over GF( <i>q</i> )

For an odd prime p and positive integers r, d such that 0 < d ≤ pr, a generic construction of d-ary 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 pr in our construction. Furthermore, the linear complexity of the proposed sequence over prime field GF(q) with the assumption of qp-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.