Open AccessThe balanced quaternary sequence of odd period with low autocorrelation
Author(s) -
Meijian Ke,
Zibi Xiao
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/2010/1/012068
Subject(s) - legendre polynomials , legendre symbol , sequence (biology) , period (music) , autocorrelation , inverse , complement (music) , mathematics , quaternary , combinatorics , prime (order theory) , physics , mathematical analysis , geometry , statistics , chemistry , geology , paleontology , quadratic equation , quadratic field , complementation , quadratic function , acoustics , gene , phenotype , biochemistry
In this paper, we construct some balanced quaternary sequences of odd period p with low autocorrelation from two types of Legendre sequences and its cyclic shift or complement and inverse Gray mapping, where p is odd prime. Firstly, we choose a Legendre sequence pair of period p, which include p ≡ 1(mod 4) and p ≡ 3(mod 4), then we get a new Legendre sequence pair of period p by cyclic shift or complement, finally, we can get a quaternary sequence of period p by utilizing inverse Gray mapping into the new Legendre sequence pair.