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

@article{Abdn2016HammingDF,
title={Hamming distances from a function to all codewords of a Generalized Reed-Muller code of order one},
author={Miriam Abd{\'o}n and R. Rolland},
journal={Applicable Algebra in Engineering, Communication and Computing},
year={2016},
volume={28},
pages={387-408}
}

Applicable Algebra in Engineering, Communication and Computing

For any finite field $${\mathbb {F}}_q$$Fq with q elements, we study the set $${\mathscr {F}}_{(q,m)}$$F(q,m) of functions from $${\mathbb {F}}_q^m$$Fqm into $${\mathbb {F}}_q$$Fq from geometric, analytic and algorithmic points of view. We determine a linear system of $$q^{m+1}$$qm+1 equations and $$q^{m+1}$$qm+1 unknowns, which has for unique solution the Hamming distances of a function in $${\mathscr {F}}_{(q,m)}$$F(q,m) to all the affine functions. Moreover, we introduce a Fourier-like… Expand