Linear Complexity of A Family of Binary $p{q}^2$-periodic Sequences From Euler Quotients

Abstract

We first introduce a family of binary $p{q}^2$-periodic sequences based on the Euler quotients modulo $pq$, where $p$ and $q$ are two distinct odd primes and $p$ divides $q-1$. The minimal polynomials and linear complexities are determined for the proposed sequences provided that $2^{q-1}\not\equiv 1\mathrm{mod}{q}^2.$ The results show that the proposed sequences have high linear complexities.

17 pages

References in corpus (1)

• On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients