Autocorrelation Values of Generalized Cyclotomic Sequences with Period <i>p</i>^<i>n</i>+1

Abstract

Recently Edemskiy proposed a method for computing the linear complexity of generalized cyclotomic binary sequences of period p n + 1 , where p = d R + 1 is an odd prime, d , R are two non-negative integers, and n > 0 is a positive integer. In this paper we determine the exact values of autocorrelation of these sequences of period p n + 1 ( n ≥ 0 ) with special subsets. The method is based on certain identities involving character sums. Our results on the autocorrelation values include those of Legendre sequences, prime-square sequences, and prime cube sequences.

Keywords

• stream cipher
• generalized cyclotomy
• generalized cyclotomic sequence
• autocorrelation value
• character sum