Classification of the $Z_{2}Z_{4}$ -Linear Hadamard Codes and Their Automorphism Groups

摘要

A -linear Hadamard code of length is a binary Hadamard code, which is the Gray map image of a -additive code with binary coordinates and quaternary coordinates. It is known that there are exactly and nonequivalent -linear Hadamard codes of length , with and , respectively, for all . In this paper, it is shown that each -linear Hadamard code with is equivalent to a -linear Hadamard code with , so there are only nonequivalent -linear Hadamard codes of length . Moreover, the order of the monomial automorphism group for the -additive Hadamard codes and the permutation automorphism group of the corresponding -linear Hadamard codes are given.