On the Automorphism Groups of the $$\mathbb{Z}_{2}\mathbb{Z}_{4}$$ -Linear Hadamard Codes and Their Classification

Abstract

It is known that there are exactly b

Double Cyclic Codes over \({\mathbb{F}_{q}+v\mathbb{F}_{q}}\)

“…As in Example 1, P v (C), P w (C), C have the parameters of [21, 5,10], [21, 10,7], [42, 15,7], respectively.…”

“…Hence, Z 2 Z 4 -additive codes generalize both the binary linear codes and the quaternary linear codes. Some good results related to Z 2 Z 4 -codes can be found in [3][4][5]. However, there are two important problems about these codes that deserve further investigation: the one is to broaden the alphabet and the other is to improve the structure of the codes further.…”

Classification of the <inline-formula> <tex-math notation="LaTeX">$Z_{2}Z_{4}$ </tex-math></inline-formula>-Linear Hadamard Codes and Their Automorphism Groups

“…The work of the second author has been partially supported by the Spanish MICINN under Grants TIN2010-17358 and TIN2013-40524-P and by the Catalan AGAUR under Grant 2014SGR-691. The material in this paper was presented in part at the 4th International Castle Meeting on Coding Theory and Applications, Palmela, Portugal, 2014 [18]. D. Krotov is with the Sobolev Institute of Mathematics, Novosibirsk 630090, Russia, and also with the Novosibirsk State University, Novosibirsk 630090, Russia (e-mail: krotov@math.nsc.ru).…”