Autocorrelation Values of Generalized Cyclotomic Sequences with Period p n +1

Xiaolin Chen and Huaning Liu
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Xiaolin Chen: School of Mathematics, Northwest University, Xi’an 710127, China
Huaning Liu: School of Mathematics, Northwest University, Xi’an 710127, China

Mathematics, 2019, vol. 7, issue 10, 1-9

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 (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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