2020/04/02 by Acar, Damla, Saraç, Bülent, Yayla, Oğuz
#Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT)
paper · doi:10.48550/arxiv.2004.00771
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.