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

Mireille Car

doi:10.4171/pm/1856

JournalspmVol. 67, No. 1pp. 13–56

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

Mireille Car
Université Aix-Marseille III, France

$Sums of $(2^r+1)$-th powers in the polynomial ring $\mathbb F_{2^m}[T]$ cover$

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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 $M \in F [T]$ by sums of $k$ -th powers. A representation

M = M_{1}^{k} + \cdot\cdot\cdot + M_{s}^{k}

of $M \in F [T]$ 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