Linear Complexity of Binary Threshold Sequences Derived from Generalized Polynomial Quotient with Prime-Power Modulus

Abstract

In this paper, firstly we extend the polynomial quotient modulo an odd prime [Formula: see text] to its general case with modulo [Formula: see text] and [Formula: see text]. From the new quotient proposed, we define a class of [Formula: see text]-periodic binary threshold sequences. Then combining the Legendre symbol and Euler quotient modulo [Formula: see text] together, with the condition of [Formula: see text], we present exact values of the linear complexity for [Formula: see text], and all the possible values of the linear complexity for [Formula: see text]. The linear complexity is very close to the period and is of desired value for cryptographic purpose. Our results extend the linear complexity results of the corresponding [Formula: see text]-periodic binary sequences in earlier work.