TY - JOUR
T1 - On Z 2s -linear Hadamard codes: kernel and partial classification
AU - Fernández-Córdoba, Cristina
AU - Vela, Carlos
AU - Villanueva, Mercè
N1 - Funding Information:
Acknowledgements This work has been partially supported by the Spanish MINECO under Grants TIN2016-77918-P (AEI/FEDER, UE) and MTM2015-69138-REDT.
Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/3/15
Y1 - 2019/3/15
N2 - The Z2s-additive codes are subgroups of Z2sn, and can be seen as a generalization of linear codes over Z 2 and Z 4 . A Z2s-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z 4 -linear Hadamard codes. In this paper, the kernel of Z2s-linear Hadamard codes of length 2 t and its dimension are established for s> 2. Moreover, we prove that this invariant only provides a complete classification for some values of t and s. The exact amount of nonequivalent such codes are given up to t= 11 for any s≥ 2 , by using also the rank.
AB - The Z2s-additive codes are subgroups of Z2sn, and can be seen as a generalization of linear codes over Z 2 and Z 4 . A Z2s-linear Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive code. It is known that the dimension of the kernel can be used to give a complete classification of the Z 4 -linear Hadamard codes. In this paper, the kernel of Z2s-linear Hadamard codes of length 2 t and its dimension are established for s> 2. Moreover, we prove that this invariant only provides a complete classification for some values of t and s. The exact amount of nonequivalent such codes are given up to t= 11 for any s≥ 2 , by using also the rank.
KW - Classification
KW - Gray map
KW - Hadamard code
KW - Kernel
KW - Z2s-additive code
KW - Z2s-linear code
UR - http://www.mendeley.com/research/z-2s-linear-hadamard-codes-kernel-partial-classification
U2 - 10.1007/s10623-018-0546-6
DO - 10.1007/s10623-018-0546-6
M3 - Article
VL - 87
SP - 417
EP - 435
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
SN - 0925-1022
IS - 2-3
ER -