Linear Complexity and k-Error Linear Complexity for p n -Periodic Sequences

Abstract

The k-error linear complexity of an N-periodic sequence with terms in the finite field \({\mathbb{F}_q}\) is defined to be the smallest linear complexity that can be obtained by changing k or fewer terms of the sequence per period. For the case that N = pfl p is an odd prime,and q is a primitive root modulo p2, we show a relationship between the linear complexity and the minimum value of k for which the k-error linear complexity is strictly less than the linear complexity.