Analysis of the k-Error Linear Complexity and Error Sequence for 2pⁿ-Periodic Binary Sequence

Abstract

The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that cause the linear complexity reduced also need to be determined. For binary sequences with period 2pⁿ, where p is an odd prime and 2 is a primitive root modulo p², we present an algorithm which computes the minimum number k such that the k-error linear complexity is not greater than a given constant c. The corresponding error sequence is also obtained.