Autocorrelation and Linear Complexity of Binary Generalized Cyclotomic Sequences with Period pq

Abstract

Ding constructed a new cyclotomic class V 0 , V 1 . Based on it, a construction of generalized cyclotomic binary sequences with period p q is described, and their autocorrelation value, linear complexity, and minimal polynomial are confirmed. The autocorrelation function C S w is 3-level if p ≡ 3 mod 4 , and C S w is 5-level if p ≡ 1 mod 4 . The linear complexity LC S > p q / 2 if p ≡ 1 mod 8 , p > q + 1 , or p ≡ 3 mod 4 or p ≡ − 3 mod 8 . The results show that these sequences have quite good cryptographic properties in the aspect of autocorrelation and linear complexity.

Linear complexity over ${\mathbb{F}_{q}}$ and 2-adic complexity of a class of binary generalized cyclotomic sequences with low-value autocorrelation

“…Example 5 Let p = 23, g = 7, r = 13. Then, = {1, 7, 9, 11, 13, 15, 25, 31, 41, 49, 51, 53, 57, 61, 63, 69, 77, 81, 83, 85, 87, 91, 95, 97, 99, 105, 109, 111, 115, 117, 121, 127, 129, 131, 135, 139, 141, 143, 145, 149, 157, 163, 165, 169, 173, 175, 177, 185, 195, 201, 211, 213, 215, 217, 219, 225}, 5,17,19,21,23,27,29,33,35,37,39,43,45,47,55,59,65,67,71,73,75,79,89,93,101,103,107,119,123,125,133,137,147,151,153,155,159,161,167,171,179,181,183,187,189,191,193,197,199,203,205,207,209,221 4,8,…”