Hamming distances from a function to all codewords of a Generalized Reed-Muller code of order one

Miriam Abdon, Robert Rolland

For any finite field ${\mathbb{F}}_q$ with $q$ elements, we study the set ${\mathcal{F}}_{(q,m)}$ of functions from ${\mathbb{F}}_q^m$ into ${\mathbb{F}}^q$. We introduce a transformat…