منابع مشابه
Monoids and Maximal Codes
In recent years codes that are not Uniquely Decipherable (UD) have been studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a monoid showing the existence, in t...
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Kraft’s inequality is a classical theorem in Information Theory which establishes the existence of prefix codes for certain (admissible) length distributions. We prove the following generalisation of Kraft’s theorem: For every admissible infinite length distribution one can construct a maximal prefix codes whose codewords satisfy this length distribution. Prefix codes are widely used in data tr...
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In this paper, we improve the best-known upper bound on the size of maximal tournament codes, and solve the related problem of edge-covering a complete graph with a minimum number of bipartite graphs of bounded size. Tournament codes are sets of {0,1,∗} strings closely related to self-synchronizing codes. We improve the current asymptotic upper bound on the size of a length-k tournament code (g...
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We investigate the possibilities for attaining two Levenshtein upper bounds for spherical codes. We find the distance distributions of all codes meeting these bounds. Then we show that the fourth Levenshtein bound can be attained in some very special cases only. We prove that no codes with an irrational maximal scalar product meet the third Levenshtein bound. So in dimensions 3 ≤ n ≤ 100 exactl...
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Several properties of the products of finite maximal prefix, maximal biprefix, semaphore, synchronous, maximal infix and maximal outfix codes are discussed respectively. We show that, for two nonempty subsets X and Y of A such that the product XY being thin, if XY is a maximal biprefix code, then X and Y are maximal biprefix codes. Also, it is shown that, for two finite nonempty subsets X and Y...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2010
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2009.09.031