TY - JOUR
T1 - Construction and classification of Z2s-linear Hadamard codes
AU - Fernández-Córdoba, C.
AU - Vela, C.
AU - Villanueva, M.
N1 - Funding Information:
Research partially supported by the Spanish MINECO under Grant TIN2013-40524-P, and by the Catalan AGAUR under Grant 2014SGR-691. 1 Email: [email protected] 2 Email: [email protected] 3 Email: [email protected]
Publisher Copyright:
© 2016 Elsevier B.V.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - The Z2s-additive and Z2Z4-additive codes are subgroups of Z2sn and Z2α×Z4β, respectively. Both families can be seen as generalizations of linear codes over Z2 and Z4. A Z2s-linear (resp. Z2Z4-linear) Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive (resp. Z2Z4-additive) code. It is known that there are exactly ⌊t−12⌋ and ⌊t2⌋ nonequivalent Z2Z4-linear Hadamard codes of length 2t, with α=0 and α≠0, respectively, for all t≥3. In this paper, new Z2s-linear Hadamard codes are constructed for s>2, which are not equivalent to any Z2Z4-linear Hadamard code. Moreover, for each s>2, it is claimed that the new constructed nonlinear Z2s-linear Hadamard codes of length 2t are pairwise nonequivalent.
AB - The Z2s-additive and Z2Z4-additive codes are subgroups of Z2sn and Z2α×Z4β, respectively. Both families can be seen as generalizations of linear codes over Z2 and Z4. A Z2s-linear (resp. Z2Z4-linear) Hadamard code is a binary Hadamard code which is the Gray map image of a Z2s-additive (resp. Z2Z4-additive) code. It is known that there are exactly ⌊t−12⌋ and ⌊t2⌋ nonequivalent Z2Z4-linear Hadamard codes of length 2t, with α=0 and α≠0, respectively, for all t≥3. In this paper, new Z2s-linear Hadamard codes are constructed for s>2, which are not equivalent to any Z2Z4-linear Hadamard code. Moreover, for each s>2, it is claimed that the new constructed nonlinear Z2s-linear Hadamard codes of length 2t are pairwise nonequivalent.
KW - Hadamard codes
KW - Z-linear codes
KW - generalized Gray map
UR - http://www.scopus.com/inward/record.url?scp=84992560385&partnerID=8YFLogxK
U2 - 10.1016/j.endm.2016.09.043
DO - 10.1016/j.endm.2016.09.043
M3 - Article
SN - 1571-0653
VL - 54
SP - 247
EP - 252
JO - Electronic Notes in Discrete Mathematics
JF - Electronic Notes in Discrete Mathematics
ER -