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Self‐dual codes and the (22,8,4) balanced incomplete block design
Author(s) -
Bilous R. T.,
van Rees G. H. J.
Publication year - 2005
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.20052
Subject(s) - combinatorial design , combinatorics , mathematics , row , block (permutation group theory) , dual (grammatical number) , automorphism , binary number , discrete mathematics , automorphism group , block design , matrix (chemical analysis) , orthogonal array , arithmetic , computer science , statistics , art , materials science , literature , database , composite material , taguchi methods
Abstract An Erratum has been published for this article in Journal of Combinatorial Designs 14: 83–83, 2006 . We enumerate a list of 594 inequivalent binary (33,16) doubly‐even self‐orthogonal codes that have no all‐zero coordinates along with their automorphism groups. It is proven that if a (22,8,4) Balanced Incomplete Block Design were to exist then the 22 rows of its incident matrix will be contained in at least one of the 594 codes. Without using computers, we eliminate this possibility for 116 of these codes. © 2005 Wiley Periodicals, Inc. J Combin Designs.