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Butson-Hadamard matrices and Plotkin-optimal p^k-ary codes (2004.00771v4)
Published 2 Apr 2020 in math.CO, cs.IT, and math.IT
Abstract: A Butson-Hadamard matrix H is a square matrix of dimension n whose entries are complex roots of unity such that HH*= nI. In the first part of this work, some new results on generalized Gray map are studied. In the second part, codes obtained from Butson-Hadamard matrices and some bounds on the minimum distance of these codes are proved. In particular, we show that the code obtained from a Butson-Hadamard matrix meets the Plotkin bound under a non-homogeneous weight. We also give the parameters of some code families which are obtained from modified Butson-Hadamard matrices under a (non)homogeneous Gray map.