Year: 2020
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Acar, Damla, Saraç, Bülent, Yayla, Oğuz
Institutions: Hacettepe University, Middle East Technical University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1702585728, G4792749414, G6074559165
OpenAlex ID: W4302008445