An Algorithm for Computing the Covering Radius of a Linear Code Based on Vilenkin-Chrestenson Transform

02/24/2022

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by   Paskal Piperkov, et al.

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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.