Premium
A class of group divisible 3‐designs and their applications
Author(s) -
Wang J.,
Ji L.
Publication year - 2009
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.20182
Subject(s) - mathematics , alphabet , combinatorics , integer (computer science) , group (periodic table) , class (philosophy) , block (permutation group theory) , block size , construct (python library) , discrete mathematics , combinatorial design , arithmetic , computer science , philosophy , linguistics , chemistry , computer security , organic chemistry , artificial intelligence , key (lock) , programming language
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
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom