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 \({\mathbb {F}}_p\).
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