On period polynomials of degree $2^m$ and weight distributions of certain irreducible cyclic codes

Ioulia N. Baoulina

doi:10.1016/j.ffa.2017.12.006

paper

On period polynomials of degree $2^{m}$ and weight distributions of certain irreducible cyclic codes

arXiv:1703.09204 · doi:10.1016/j.ffa.2017.12.006

Abstract

We explicitly determine the values of reduced cyclotomic periods of order $2^{m}$ , $m \geq 4$ , for finite fields of characteristic $p \equiv 3$ or $5 (mod 8)$ . These evaluations are applied to obtain explicit factorizations of the corresponding reduced period polynomials. As another application, the weight distributions of certain irreducible cyclic codes are described.

17 pages, 5 tables

On period polynomials of degree 2m and weight distributions of certain irreducible cyclic codes

Abstract

On period polynomials of degree $2^{m}$ and weight distributions of certain irreducible cyclic codes