A class of binary sequences with period pq is constructed using generalized cyclotomic classes, and their autocorrelation distribution and 2-adic complexity are determined using Gauss sum and group ring theory. The results show that the autocorrelation function of the new sequences is 3-level if p ≡ 3 (mod 4) and q ≡ 3 (mod 4) which is very close to the optimal and the 2-adic complexity of these sequences is maximum if p < q < 2p − 1. According to the rational approximation algorithm(RAA), these sequences have quite good cryptographic properties in the aspect of autocorrelation and 2-adic complexity.

In coding theory, quasi λ-cyclic codes form an important class of codes which have been extensively studied. In this paper, we investigate the algebraic structure of quasi λ-cyclic codes over finite commutative semi simple rings. And we establish the relationship between quasi λ-cyclic codes over finite commutative semi-simple ring R and quasi λ-cyclic codes over finite fields Fq. Furthermore, we decompose quasi λ-cyclic codes to a direct sum of component codes C linear codes over rings, give the decomposition of quasi λ-cyclic codes and describe its dual codes.