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Self-dual codes and the (22,8,4) balanced incomplete block design

✍ Scribed by R. T. Bilous; G. H. J. van Rees

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 142 KB
Volume: 13
Category: Article
ISSN: 1063-8539
DOI: 10.1002/jcd.20052

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✦ Synopsis

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.

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