# Sums of $(2_{r}+1)$-th powers in the polynomial ring $F_{2_{m}}[T]$

### Mireille Car

Université Aix-Marseille III, France

## Abstract

Let $F$ be a finite field with $2_{m}$ elements and let $k=2_{r}+1$. We study representations and strict representations of polynomials $M∈F[T]$ by sums of $k$-th powers. A representation

$M=M_{1}+⋅⋅⋅+M_{s}$

of $M∈F[T]$ as a sum of $k$-th powers of polynomials is strict if $k deg M_{i}<k+deg M$.

## Cite this article

Mireille Car, Sums of $(2_{r}+1)$-th powers in the polynomial ring $F_{2_{m}}[T]$. Port. Math. 67 (2010), no. 1, pp. 13–56

DOI 10.4171/PM/1856