Sums of (2^<var>r<var>&#8201;+&#8201;1)-th powers in the polynomial ring <b>F</b>_{2^<var>m</var>}[<var>T</var>]

Abstract

supp { vertical-align: 0.8ex; font-size:75%; } subb { vertical-align: -0.8ex; font-size:75%; } .ions { line-height: 1.8; } .ions subb {position: relative; top: 4; left: 1; } .ions supp {position: absolute; top: 70; left:985; } Let F be a finite field with 2m elements and let k = 2r + 1. We study representations and strict representations of polynomials M ∈ F[T] by sums of k-th powers. A representation

M = Mk1 + ··· + Mks

of M ∈ F[T] as a sum of k-th powers of polynomials is strict if k deg Mi < k + deg M.