Filmus, Yuval - Universal codes of the natural numbers

lmcs:975 - Logical Methods in Computer Science, August 29, 2013, Volume 9, Issue 3
Universal codes of the natural numbers

Authors: Filmus, Yuval

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.

Source :
DOI : 10.2168/LMCS-9(3:7)2013
Volume: Volume 9, Issue 3
Published on: August 29, 2013
Submitted on: October 16, 2012
Keywords: Computer Science - Logic in Computer Science,Computer Science - Information Theory


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