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An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform (2202.12111v1)
Published 24 Feb 2022 in cs.IT, cs.DM, math.CO, and math.IT
Abstract: We present a generalization of Walsh-Hadamard transform that is suitable for applications in Coding Theory, especially for computation of the weight distribution and the covering radius of a linear code over a finite field. The transform used in our research, is a modification of Vilenkin-Chrestenson transform. Instead of using all the vectors in the considered space, we take a maximal set of nonproportional vectors, which reduces the computational complexity.
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