Hamming distances from a function to all codewords of a Generalized ReedMuller code of order one
Abstract
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 transformation that allows us to determine a linear system of $q^{m+1}$ equations and $q^{m+1}$ unknowns, which has for solution the Hamming distances of a function in ${\mathcal F}_{(q,m)}$ to all the affine functions.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.04788
 Bibcode:
 2015arXiv151204788A
 Keywords:

 Computer Science  Information Theory;
 11T71;
 94B05