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.