The Properties of the 1-error Linear Complexity of pn-periodic Sequences Over Fp

Abstract

Some properties of pⁿ-periodic sequences over F_p with fixed linear complexity value are found. Based on this, the distribution of the 1-error linear complexity of pⁿ-periodic sequences over F_p is provided. The expectation of the 1-error linear complexity of random pⁿ-periodic sequences over F_p is calculated and its estimated range is given. According to these results, an efficient algorithm for computing the 1-error linear complexity of a pⁿ-periodic sequence, as well as a new algorithm for determining all the error vectors that give the 1-error linear complexity, is proposed