Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length N is called Z-optimal if its zero correlation zone width can achieve the maximum value (N + 1)/2. In this letter, inserting three elements to a GCP of length L, or deleting a point of a GCP of length L, we propose two constructions of Z-optimal ZCPs with length L + 3 and L - 1, where L=2α 10β 26γ, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

AlphaSeq is a new paradigm to design sequencess with desired properties based on deep reinforcement learning (DRL). In this work, we propose a new metric function and a new reward function, to design an improved version of AlphaSeq. We show analytically and also through numerical simulations that the proposed algorithm can discover sequence sets with preferable properties faster than that of the previous algorithm.

Codebooks with small maximal cross-correlation amplitudes have important applications in code division multiple access (CDMA) communication, coding theory and compressed sensing. In this letter, we design a new codebook based on a construction of Ramanujan graphs over finite abelian groups. We prove that the new codebook with length K=q+1 and size N=q2+2q+2 is asymptotically optimal with nearly achieving the Levenshtein bound when n=3, where q is a prime power. The parameters of the new codebook are new.

The objective of this letter is to present a family of q-ary codes with parameters $[rac{q^m-1}{q-1},rac{q^m-1}{q-1}-2m,d]$, where m is a positive integer, q is a power of an odd prime and 4≤d≤5. The parameters are proved to be optimal or almost optimal with respect to an upper bound on linear codes.