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There exists no (15,5,4) RBIBD † *
Author(s) -
Kaski Petteri,
Östergård Patric R. J.
Publication year - 2001
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.1016
Subject(s) - cardinality (data modeling) , combinatorics , mathematics , clique , equidistant , existential quantification , code (set theory) , block (permutation group theory) , discrete mathematics , set (abstract data type) , computer science , geometry , programming language , data mining
An ( n , M , d ) q code is a q ‐ary code of length n , cardinality M , and minimum distance d . We show that there exists no (15,5,4) resolvable balanced incomplete block design (RBIBD) by showing that there exists no (equidistant) (14,15,10) 3 code. This is accomplished by an exhaustive computer search using an orderly algorithm combined with a maximum clique algorithm. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 357–362, 2001