2 research outputs found
Hamming distances from a function to all codewords of a Generalized Reed-Muller code of order one
International audienceFor any finite field with elements, we study the set of functions from into from geometric, analytic and algorithmic points of view.We determine a linear system of equations and unknowns, which has for unique solution the Hamming distances of a function in to all the affine functions. Moreover,we introduce a Fourier-like transform which allows us to compute all these distances at a cost and which would be useful for further problems