The balanced quaternary sequence of odd period with low autocorrelation

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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.