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Vietnam
Journal of Mathematics 39:2 (2011) 159-176
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On Codes Defined by Binary Relations
Part I: Embedding Problem
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Do Long Van1 and Kieu Van Hung2
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1 Institute
of Mathematics, 18 Hoang Quoc Viet, Hanoi,
Vietnam
2The Office of Government, 01
Hoang Hoa Tham, Hanoi, Vietnam
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Abstract. We consider the possibility to embed a finite
(regular) code of a given class C
of codes in a code maximal in C
(not necessarily maximal as a code) which remains finite (regular, respectively).
A general embedding schema is proposed for the classes of codes, which can
be defined by length-increasing transitive binary relations. As
applications, positive solutions for the embedding problem are obtained in
a unified way for many classes of codes, well-known as well as new.
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2000 Mathematics
Subject Classification. 94A45, 68Q45.
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Keywords. Code,
embedding problem, independent set, tree representation.
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Email: hungkvs@gmail.com [Corresponding
Author]
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Established
by Vietnam Academy of Science and Technology & Vietnam Mathematical
Society
Published
by Springer since January 2013
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