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.

In frequency-hopping (FH) multiple access systems, frequency-hopping sequences (FHSs) with optimal Hamming correlation properties are needed. Based on the d-form functions with ideal autocorrelation properties, a new set of FHSs is constructed. The new FHS set is optimal with respect to the Peng-Fan bounds and each FHS in the set is optimal with respect to the Lempel-Greenberger bound.

In this letter, we examine the linear complexity of some 3-ary sequences, proposed by No, of period 3n-1(n=3ek, e, k integer) with the ideal autocorrelation property. The exact value of linear complexity k(6e)w is determined when the parameter r =. Furthermore, the upper bound of the linear complexity is given when the other forms of the value r is taken. Finally, a Maple program is designed to illustrate the validity of the results.

A new subfamily of sequences with optimal correlation properties is constructed for the generalized Kasami set. A lower bound on the linear span is established. It is proved that with suitable choices of parameters, this subfamily has exponentially larger linear spans than either No sequences or TN sequences. A class of sequences with ideal autocorrelation is also proved to have large linear span.

In this paper, a new family S(r) of 2n binary sequences of period 2n-1 is proposed, where n ≡ 2 mod 4 and gcd(r, 2n/2-1)=1. The presented family takes 4-valued out-of-phase auto- and cross-correlation values -1, 2n/2-1, and 2n/2+1-1, and its correlation distribution is determined. For r=2(n-2)/4-1, each sequence in S(r), except the unique ideal autocorrelation sequence in the family, is proved to have a large linear span n2n/2-2, whilst the linear span of the latter is n2(n-2)/4-1.