Construction of binary almost perfect sequences based on extended cyclic difference sets

Sequences with noise-like characteristics are required for symbol synchronization, signal detection, signal estimation, spectrum spreading and secrecy coding. Periodic binary sequences exhibiting zero out-of-phase autocorrelation except one value in the middle are studied here. They are based mainly on cyclic difference sets D with parameters (v,k,λ), where k denotes the number of elements in D and λ the number of distinct differences modulo v between the elements in D. Those difference sets are perfect if the additional relation v=k(k-1)/λ+1 applies. This paper describes a family of binary sequences derived from extended perfect cyclic difference sets with parameters (n=v+1,k,λ) where n is the period of the sequence. The linear complexity of these binary sequences is approximately n/2. Many binary pseudo-noise sequences of period N=2^m-1 generated by m-stage linear feedback shift registers can be modified to correspond to an extended cyclic difference set with parameters (n=2^m, k=2 ^m-1-1, λ=2^m-2-1) and exhibiting a three-valued autocorrelation function. This modification increases the linear complexity of these pseudo-random sequences from m to approximately 2^m-1. Applications in spread spectrum techniques and cryptography can be expected