New Quaternary Sequences with Ideal Autocorrelation Constructed from Legendre Sequences

Young-Sik KIM  Ji-Woong JANG  Sang-Hyo KIM  Jong-Seon NO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.9   pp.1872-1882
Publication Date: 2013/09/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1872
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Spread Spectrum Technologies and Applications
autocorrelation,  ideal autocorrelation,  legendre sequences,  quaternary sequences,  sequences,  

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In this paper, for an odd prime p, new quaternary sequences of even period 2p with ideal autocorrelation property are constructed using the binary Legendre sequences of period p. For the new quaternary sequences, two properties which are considered as the major characteristics of pseudo-random sequences are derived. Firstly, the autocorrelation distribution of the proposed quaternary sequences is derived and it is shown that the autocorrelation values of the proposed quaternary sequences are optimal. For both p≡1 mod 4 and p≡3 mod 4, we can construct optimal quaternary sequences while only for p≡3 mod 4, the binary Legendre sequences can satisfy ideal autocorrelation property. Secondly, the linear complexity of the proposed quaternary sequences is also derived by counting non-zero coefficients of the discrete Fourier transform over the finite field Fq which is the splitting field of x2p-1. It is shown that the linear complexity of the quaternary sequences is larger than or equal to p or (3p+1)/2 for p≡1 mod 4 or p≡3 mod 4, respectively.