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On the Maximum Size of a Prefix Code
  • Peter Horák ,
  • Viliam Hromada ,
  • Otokar Grošek
Peter Horák
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Viliam Hromada
Slovak University of Technology in Bratislava

Corresponding Author:[email protected]

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Otokar Grošek
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Abstract

In this paper, we investigate the maximum size of a minimal dictionary of a binary prefix-code string. We develop exact formulas for the maximum number of codewords of a minimal dictionary, which belongs to a binary string of some length. Further, we elaborate on the computational complexity of our approach and its relation to the Lambert function. We also present a way, how this information enables us to efficiently construct a Huffman code in the case of uniform probability distribution of codewords.
The paper is of mathematical nature, i.e. all the methodology used in the paper is based on mathematical proofs.
May 2023Published in IEEE Transactions on Information Theory volume 69 issue 5 on pages 2855-2859. 10.1109/TIT.2023.3236688