Ju l 2 00 6 Reducing the Computation of Linear Complexities of Periodic Sequences

The linear complexity of a periodic sequence over GF (p) play an important role in cryptography and communication([1]). In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of an arbitrary period un (where u|p−1, gcd(n, p −1) = 1) sequence over GF (p) to the computation of the linear complexities and minimal connection polynomials of u period n sequences over GF (p). Some applications of this reduction in the fast algorithm for determining the linear complexity and minimal connection polynomials are presented.