Some Notes on Pseudorandom Binary Sequences Derived from Fermat-Euler Quotients

Abstract

For an odd prime p and a positive integer r, new classes of binary sequences with period p^r+1 are proposed from Euler quotients in this letter, which include several known classes of binary sequences derived from Fermat quotients and Euler quotients as special cases. The advantage of the new constructions is that they allow one to choose their support sets freely. Furthermore, with some constrains on the support set, the new sequences are proved to possess large linear complexities under the assumption of 2^p-1 ≢ 1 mod p².