A class of group divisible 3-designs and their applications

✍ Scribed by J. Wang; L. Ji

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 119 KB
• Volume: 17
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/jcd.20182

✦ Synopsis

Abstract

In this article, we first show that a group divisible 3‐design with block sizes from {4, 6}, index unity and group‐type 2^m^ exists for every integer m≥ 4 with the exception of m = 5. Such group divisible 3‐designs play an important role in our subsequent complete solution to the existence problem for directed H‐designs DH~λ~(m, r, 4, 3)s. We also consider a way to construct optimal codes capable of correcting one deletion or insertion using the directed H‐designs. In this way, the optimal single‐deletion/insertion‐correcting codes of length 4 can be constructed for all even alphabet sizes. © 2008 Wiley Periodicals, Inc. J Combin Designs 17: 136–146, 2009