Release time:2025-03-31

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DOI number:10.1007/s00200-014-0214-7

Journal:APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING

Key Words:Cyclotomic sequence;Legendre symbol;Linear complexity;Autocorrelation;Crosscorrelation

Abstract:Let be distinct odd primes and let be positive integers. Based on cyclotomic classes proposed by Ding and Helleseth (Finite Fields Appl 4:140-166, 1998), a binary cyclotomic sequence of period is defined and denoted by . The linear complexity of is determined and is proved to be greater than or equal to . The autocorrelation function of is explicitly computed. Let . We also explicitly compute the crosscorrelation function of and the Legendre sequence with respect to . It is shown that and have two-level or three-level crosscorrelation, and all their two-level crosscorrelation functions are determined.

Co-author:Ying Gao

First Author:Lin Wang

Indexed by:Journal paper

Correspondence Author:Lin Wang

Volume:25

Issue:1-2

Page Number:67-97

ISSN No.:0938-1279

Translation or Not:no

Date of Publication:2014-03-08