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VOLUME 9, ISSUE 3, PAPER 7


Universal codes of the natural numbers

©Yuval Filmus, University of Toronto

Abstract
A code of the natural numbers is a uniquely-decodable binary code of the natural numbers with non-decreasing codeword lengths, which satisfies Kraft's inequality tightly. We define a natural partial order on the set of codes, and show how to construct effectively a code better than a given sequence of codes, in a certain precise sense. As an application, we prove that the existence of a scale of codes (a well-ordered set of codes which contains a code better than any given code) is independent of ZFC.

Publication date: August 29, 2013

Full Text: PDF | PostScript
DOI: 10.2168/LMCS-9(3:7)2013

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