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.
Highlights
Pseudorandom sequences with good randomness properties are widely applied in simulation, radar systems, spread-spectrum communication systems, ranging systems, software testing, global positioning systems, channel coding, code-division multiple-access (CDMA) systems, and stream ciphers [1,2,3,4,5]
In contrast to [11,12,13], we present a simpler proof by using certain identities involving character sums
In this paper we computed the exact values of autocorrelation of generalized cyclotomic binary sequences of any order d and period pn+1 (n ≥ 0)
Summary
Pseudorandom sequences with good randomness properties are widely applied in simulation, radar systems, spread-spectrum communication systems, ranging systems, software testing, global positioning systems, channel coding, code-division multiple-access (CDMA) systems, and stream ciphers [1,2,3,4,5]. Sun, and Xiao [10] studied new generalized cyclotomic binary sequences with respect to p2 , which are a special case of those whose characteristic set are {0} ∪ [∪d|n,d>1 nd D1 ] in [6] Results indicate that these sequences possess high linear complexity. The exact same results on the linear complexity and the exact values of autocorrelation of these new binary sequences were presented in [11,12], respectively. Song [13] calculated the exact values of autocorrelation and linear complexity of prime cube sequences with period p3. In 2011 Edemskiy [20] proposed a method for computing the linear complexity of pn+1 -periodic generalized cyclotomic binary sequences. Compute the exact values of autocorrelation of this special generalized cyclotomic sequence with period p n +1 ( n ≥ 0 )
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
