Reducing the Computation of Linear Complexities of Periodic Sequences over GF(pm)

The linear complexity of a periodic sequence over GF (pm) plays an important role in cryptography and communication [12]. In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of a period un sequence over GF (pm) to the computation of the linear complexities and minimal connection polynomials of u period n sequences. The conditions u|pm − 1 and gcd(n, pm − 1) = 1 are required for the result to hold. Some applications of this reduction in fast algorithms to determine the linear complexities and minimal connection polynomials of sequences over GF (pm) are presented.