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On the Maximum Size of a Prefix Code

preprint
posted on 01.06.2022, 08:36 authored by Peter Horák, Viliam HromadaViliam Hromada, Otokar Grošek
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.

Funding

NATO Science for Peace and Security Programme under Grant G5448

History

Email Address of Submitting Author

viliam.hromada@stuba.sk

ORCID of Submitting Author

0000-0001-9767-7728

Submitting Author's Institution

Slovak University of Technology in Bratislava

Submitting Author's Country

Slovakia