Intersection Matrices for Partitions by Binary Perfect Codes
IEEE Transactions on Information Theory, vol. IT-47, pp. 1621-1624, May 2001.
Sergey AVGUSTINOVICH (#), Antoine LOBSTEIN (*), Faina SOLOV'EVA (#)
(#) Sobolev Institute of Mathematics
Siberian Division of Russian Academy of Science
prospekt Koptyuga 4, Novosibirsk 630090, Russia
(*) Centre National de la Recherche Scientifique
Ecole Nationale Supérieure des Télécommunications
46 rue Barrault, 75634 Paris cédex 13, France
Abstract. We investigate the following problem: given two partitions of the Hamming space, their intersection matrix provides the cardinalities of the pairwise intersections of the subsets of these partitions. If we consider partitions by extended perfect codes, how many intersection matrices can we construct?
Acknowledgment. Antoine Lobstein is indebted to Faina Solov'eva for inviting him for a one-month stay at the Sobolev Institute of Mathematics.