Partitions of the 8‐dimensional vector space over  GF (2) | Zendy

ElZanati S. | Zendy; Heden O. | Zendy; Seelinger G. | Zendy; Sissokho P. | Zendy; Spence L. | Zendy; Eynden C. Vanden | Zendy

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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

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