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Partitions of the 8‐dimensional vector space over GF (2)
Author(s) -
ElZanati S.,
Heden O.,
Seelinger G.,
Sissokho P.,
Spence L.,
Eynden C. Vanden
Publication year - 2010
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20247
Subject(s) - linear subspace , mathematics , partition (number theory) , combinatorics , tuple , vector space , dimension (graph theory) , subspace topology , normed vector space , space (punctuation) , discrete mathematics , pure mathematics , mathematical analysis , computer science , operating system
Let V = V ( n, q ) denote the vector space of dimension n over GF ( q ). A set of subspaces of V is called a partition of V if every nonzero vector in V is contained in exactly one subspace of V . Given a partition of V with exactly a i subspaces of dimension i for 1≤ i ≤ n , we have , and we call the n ‐tuple ( a n , a n − 1 , …, a 1 ) the type of . In this article we identify all 8‐tuples ( a 8 , a 7 , …, a 2 , 0) that are the types of partitions of V (8, 2). © 2010 Wiley Periodicals, Inc. J Combin Designs 18: 462–474, 2010