A note on regular subgroups of the automorphism group of the linear Hadamard code

07/12/2018

∙

by   I. Yu. Mogilnykh, et al.

∙

0

∙

share

We consider the regular subgroups of the automorphism group of the linear Hadamard code. These subgroups correspond to the regular subgroups of GA(r,2), w.t.r action on the vectors of F_2^r, where n=2^r-1 is the length of the Hamadard code. We show that the dihedral group D_2^r-1 is a regular subgroup of GA(r,2) only when r=3. Following the approach of M we study the regular subgroups of the Hamming code obtained from the regular subgroups of the automorphism group of the Hadamard code of length 15.