On the intersection of Z2Z4-additive Hadamard codes

Authors:
Josep Rifà;Faina I. Solov'eva;Mercè Villanueva
Affiliations:
Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Bellaterra, Spain;Sobolev Institute of Mathematics and the Novosibirsk State University, Novosibirsk, Russia;Department of Information and Communications Engineering, Universitat Autònoma de Barcelona, Bellaterra, Spain
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

The intersection structure for Z2Z4-additive Hadamard codes is investigated. For any two of these codes C1 and 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 Z2Z4-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.