A quaternary sequence is constructed by Gray mapping of a binary sequence with even period and its shift. The autocorrelation of the new quaternary sequence is the same as that of the binary sequence employed. Quaternary sequences with the maximum autocorrelation 2 can be obtained by the construction for period N≡ 2 ( mod 4).

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.

We propose an extension method of quaternary low correlation zone (LCZ) sequence set with odd period. From a quaternary LCZ sequence set with parameters (N, M, L, 1), the proposed method constructs a new quaternary LCZ sequence set with parameters (2N, 2M, L, 2), where N is odd. If the employed LCZ sequence set in the construction is optimal, the extended LCZ sequence set becomes also optimal where N = kL, L > 4, and k>2.

In this paper, given an integer e and n such that e|n, and a prime p, we propose a method of constructing optimal p2-ary low correlation zone (LCZ) sequence set with parameters (pn-1, pe-1, (pn -1)/(pe -1), 1) from a p-ary sequence of the same length with ideal autocorrelation. The resulting p2-ary LCZ sequence set can be viewed as the generalization of the optimal quaternary LCZ sequence set by Kim, Jang, No, and Chung in respect of the alphabet size. This generalization becomes possible due to a completely new proof comprising any prime p. Under this proof, the quaternary case can be considered as a specific example for p = 2.

In this paper, using p-ary bent functions defined on vector space over the finite field Fpk, we generalized the construction method of the families of p-ary bent sequences with balanced and optimal correlation properties introduced by Kumar and Moreno for an odd prime p, called generalized p-ary bent sequences. It turns out that the family of balanced p-ary sequences with optimal correlation property introduced by Moriuchi and Imamura is a special case of the newly constructed generalized p-ary bent sequences.

In this letter, we propose a new construction of quaternary low correlation zone (LCZ) sequence set using binary LCZ sequence sets and an inverse Gray mapping. The new construction method provides optimal quaternary LCZ sequence sets even if the employed binary LCZ sequence set is suboptimal. The optimality is improved at the price of alphabet extension.