On the autocorrelation and the linear complexity of q-ary prime n-square sequences

Abstract

Cryptographically strong sequences should have long periods, large linear complexity, low correlation, and balance properties. In this paper, we determine the autocorrelation of the q-ary prime n-square sequences with length p n , where p is an odd prime, n is a positive integer and q is a divisor of p-1. When q is a prime, we also determine the linear complexity of the prime n-square sequences over the prime field Fq . It is shown that these sequences have good linear complexity and balance properties, but don't have desirable autocorrelation properties. © 2010 Springer-Verlag.