On the Intersection of Z(2)Z(4)-Additive Hadamard Codes
The intersection structure for Z(2)Z(4)-additive Hadamard codes is investigated. For any two of these codes C(1) and C(2), the Abelian group structure of the intersection C(1) boolean AND C(2) 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 Z(2)Z(4)-additive Hadamard codes C(1) and C(2) 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.
hadamard codes additive codes extended perfect codes perfect codes