Linear complexity of Whiteman’s generalized cyclotomic sequences of order 2k

Abstract

Let $p_1$ and $p_2$ be two odd distinct primes such that $\mathrm{gcd}(p_1-1,p_2-1)=2k$. In this correspondence, we calculate the accurate value of the minimal polynomial of Whiteman's generalized cyclotomic sequences of order $2k$ over galois field $\mathrm{GF}(q)$, where $k\geq 1$ and $q=p^m$ and $p$ is an odd prime and $m$ is an integer. We calculate the linear complexity of these sequences. We get, the linear complexity is large. So, these sequences with high linear complexity are widely used in many areas such as combinatorics, cryptography and coding theory.