s-PD sets, rank and kernel of Hadamard codes and construction of Hadamard codes using magma
Abstract
This article presents the recursive construction of s-PD sets, a special subset of the permutation automorphism group of a code, which enables the correction of s errors of binary linear Hadamard codes over the field F4. We discuss the rank and kernel of these Hadamard codes. We develop new MAGMA functions to generate Hadamard codes over the field F4. We also give MAGMA functions to find the minimum distance and generator matrix of a Hadamard code over F4.
Copyright © 2020 Briji J. Chathely, Rajendra P. Deore. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
B. J. Chathely, R. P. Deore, s-PD sets, rank and kernel of Hadamard codes and construction of Hadamard codes using magma, J. Math. Comput. Sci. 10 (2020), 1510–1528. https://doi.org/10.28919/jmcs/4664
BibTeX
@article{Chathely2020,
author = {Chathely, Briji J. and Deore, Rajendra P.},
title = {s-PD sets, rank and kernel of Hadamard codes and construction of Hadamard codes using magma},
journal = {J. Math. Comput. Sci.},
volume = {10},
year = {2020},
pages = {1510--1528},
doi = {10.28919/jmcs/4664}
}