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Existence of T*(3, 4,v)-codes

✍ Scribed by J. Wang; L. Ji

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
136 KB
Volume
13
Category
Article
ISSN
1063-8539

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✦ Synopsis

Abstract

A word of length k over an alphabet Q of size v is a vector of length k with coordinates taken from Q. Let Q^*^~4~ be the set of all words of length 4 over Q. A T^*^(3, 4, v)‐code over Q is a subset C^*^βŠ† Q^*^~4~ such that every word of length 3 over Q occurs as a subword in exactly one word of C^*^. Levenshtein has proved that a T^*^(3, 4, v____v)‐code exists for all even v. In this paper, the notion of a generalized candelabra t‐system is introduced and used to show that a T^*^(3, 4, v)‐code exists for all odd v. Combining this with Levenshtein's result, the existence problem for a T^*^(3,4, v)‐code is solved completely. Β© 2004 Wiley Periodicals, Inc. J Combin Designs 13: 42–53, 2005.

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