On the Distribution of p-Error Linear Complexity of p-Ary Sequences with Period pⁿ

Abstract

Linear complexity and the k-error linear complexity of periodic sequences are the important security indices of stream cipher systems. This paper focuses on the distribution of p-error linear complexity of p-ary sequences with period pⁿ. For p-ary sequences of period pⁿ with linear complexity pⁿ-p+1, n≥1, we present all possible values of the p-error linear complexity, and derive the exact formulas to count the number of the sequences with any given p-error linear complexity.