Fast algorithms for determining the linear complexities of sequences over GF(p m) with the period 3n

Abstract

In this paper, for the the primes p such that 3 is a divisor of p -1, we prove a result which reduces the computation of the linear complexity of a sequence over GF ( p m ) (any positive integer m ) with the period 3 n ( n and p m -1 are coprime) to the computation of the linear complexities of three sequences with the period n . Combined with some known algorithms such as generalized Games-Chan algorithm, Berlekamp-Massey algorithm and Xiao-Wei-Lam-Imamura algorithm, we can determine the linear complexity of any sequence over GF ( p m ) with the period 3 n ( n and p m -1 are coprime) more efficiently.