Summary
The 2018 International Symposium on Information Theory and Its Applications (ISITA2018)
2018
Session Number:We-AM-Poster
Session:
Number:We-AM-Poster.7
Some properties of NTU sequences
Gangsan Kim, Hong-Yeop Song,
pp.497-497
Publication Date:2018/10/18
Online ISSN:2188-5079
DOI:10.34385/proc.55.We-AM-Poster.7
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Summary:
We will fix following notation throughout the paper. q and n are each a odd prime power and an integer larger than 1. Fq and Fqn are the finite fields with q and qn elements, respectively. α is a primitive element of Fqn. Trn1 (x) 2 Fq is the trace of x ∈ Fqn defined by Trn1 (x) = Pn??1 i=0 xqi . ?X(x) ∈ {-1,0,1｝is a quadratic character of x ∈ Fq defined as 0 when x is 0, 1 when x is a quadratic element over Fq, and -1 otherwise. The periodic autocorrelation function of a binary sequence s = {st | t = 0, 1, 2, ...} of period L is defined by Cs(?t) = PL??1 t=0 (??1)st+st+? . A binary sequence s = {st | t = 0, 1, 2,...} of period 2L is a anti-periodic if st + st+L = 1, for all t. The NTU sequences s = {st| t = 0, 1, 2,...} proposed in [3] are defined by st = - 1; ?(Trn1 (?t)) = 1 0; otherwise The NTU sequences have period of 2(qn - 1)/(q - 1) and 3-level autocorrelation property. Its’ autocorrelation profile is exactly shown in [3].