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Conflict-avoiding codes and cyclic triple systems.
- Source :
-
Problems of Information Transmission . Sep2007, Vol. 43 Issue 3, p199-212. 14p. - Publication Year :
- 2007
-
Abstract
- Abstract  The paper deals with the problem of constructing a code of the maximum possible cardinality consisting of binary vectors of length n and Hamming weight 3 and having the following property: any 3 � n matrix whose rows are cyclic shifts of three different code vectors contains a 3 � 3 permutation matrix as a submatrix. This property (in the special case w = 3) characterizes conflict-avoiding codes of length n for w active users, introduced in [1]. Using such codes in channels with asynchronous multiple access allows each of w active users to transmit a data packet successfully in one of w attempts during n time slots without collisions with other active users. An upper bound on the maximum cardinality of a conflict-avoiding code of length n with w = 3 is proved, and constructions of optimal codes achieving this bound are given. In particular, there are found conflict-avoiding codes for w = 3 which have much more vectors than codes of the same length obtained from cyclic Steiner triple systems by choosing a representative in each cyclic class. [ABSTRACT FROM AUTHOR]
- Subjects :
- *STEINER systems
*BLOCK designs
*RACING shells
*MATRICES (Mathematics)
Subjects
Details
- Language :
- English
- ISSN :
- 00329460
- Volume :
- 43
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Problems of Information Transmission
- Publication Type :
- Academic Journal
- Accession number :
- 27314614
- Full Text :
- https://doi.org/10.1134/S0032946007030039