Trace representation of Legendre sequences over non-binary fields

Abstract

For distinct odd primes N and p, we view the N-periodic binary Legendre sequence as a p-ary sequence and present its trace representation via trace functions over \({\mathbb {F}}_p\). We use a skill to calculate the Mattson–Solomon polynomials of Legendre sequences and then describe the Mattson–Solomon polynomials by means of trace functions over \({\mathbb {F}}_p\).