New Quaternary Sequences with Even Period and Three-Valued Autocorrelation

Jin-Ho CHUNG  Yun Kyoung HAN  Kyeongcheol YANG  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E93-A   No.1   pp.309-315
Publication Date: 2010/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E93.A.309
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Coding Theory
Keyword: 
autocorrelation,  Gray map,  periodic sequences,  quaternary sequences,  Sidel'nikov sequences,  

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Summary: 
In this paper we present a construction method for quaternary sequences from a binary sequence of even period, which preserves the period and autocorrelation of the given binary sequence. By applying the method to the binary sequences with three-valued autocorrelation, we construct new quaternary sequences with three-valued autocorrelation, which are balanced or almost balanced. In particular, we construct new balanced quaternary sequences whose autocorrelations are three-valued and have out-of-phase magnitude 2, when their periods are N=pm-1 and N≡ 2 (mod 4) for any odd prime p and any odd integer m. Their out-of-phase autocorrelation magnitude is the known optimal value for N≠ 2,4,8, and 16.