TY - JOUR
T1 - On the intersection of ℤ2ℤ4-additive Hadamard codes
AU - Rifa, Josep
AU - Solov'eva, Faina I.
AU - Villanueva, Mercè
N1 - Funding Information:
Manuscript received March 25, 2008; revised October 04, 2008. Current version published March 18, 2009. This work was supported in part by the Spanish MEC and the European FEDER under Grants MTM2006-03250 and PCI2006-A7-0616. J. Rifà and M. Villanueva are with the Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, 08193-Bellaterra, Spain (e-mail: [email protected]; merce.villanueva@ autonoma.edu). F. I. Solov’eva is with the Sobolev Institute of Mathematics and the Novosibirsk State University, 630090 Novosibirsk, Russia (e-mail: [email protected]). Communicated by T. Etzion, Associate Editor for Coding Theory. Digital Object Identifier 10.1109/TIT.2009.2013037
PY - 2009
Y1 - 2009
N2 - The intersection structure for ℤ2ℤ4 -additive Hadamard codes is investigated. For any two of these codes C1 C2, the Abelian group structure of the intersection C1 ∩ C2 is characterized. The parameters of this Abelian group structure corresponding to the intersection codes are computed, establishing lower and upper bounds for them. Constructions are given of codes whose intersection has any parameters between these bounds. Finally, the intersection problem, i.e., what the possibilities are for the number of codewords in the intersection of two ℤ2 ℤ4-additive Hadamard codes C1 and C2 being of the same length, is also studied. Lower and upper bounds for the intersection number are established and, for any value between these bounds, codes with this intersection value are constructed.
AB - The intersection structure for ℤ2ℤ4 -additive Hadamard codes is investigated. For any two of these codes C1 C2, the Abelian group structure of the intersection C1 ∩ C2 is characterized. The parameters of this Abelian group structure corresponding to the intersection codes are computed, establishing lower and upper bounds for them. Constructions are given of codes whose intersection has any parameters between these bounds. Finally, the intersection problem, i.e., what the possibilities are for the number of codewords in the intersection of two ℤ2 ℤ4-additive Hadamard codes C1 and C2 being of the same length, is also studied. Lower and upper bounds for the intersection number are established and, for any value between these bounds, codes with this intersection value are constructed.
KW - Additive codes
KW - Extended perfect codes
KW - Hadamard codes
KW - Perfect codes
UR - http://www.scopus.com/inward/record.url?scp=64249137058&partnerID=8YFLogxK
U2 - 10.1109/TIT.2009.2013037
DO - 10.1109/TIT.2009.2013037
M3 - Article
AN - SCOPUS:64249137058
SN - 0018-9448
VL - 55
SP - 1766
EP - 1774
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 4
ER -