Abstract
The paper deals with the code length distributions for which the proportion of the codewords of a given length to all words of this length is a suitable power of 1/2. We derive a lower bound and an upper bound for the number of prefix codes with the above property. We also investigate the ratio of prefix codes to all uniquely decodable codes, which relates to the more general results of Woryna (Discret Math 340(2):51–57, 2017; Discret Appl Math 244:205–213, 2018).
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Acknowledgements
The authors would like to thank the referees for their very careful reading on this paper and helpful comments. This work was supported by the Fundamental Research Funds for the Central Universities, and the Research Funds of Renmin University of China (No. 2020030254).
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Communicated by L. Storme.
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Xu, J., Zheng, Z., Tian, K. et al. Two properties of prefix codes and uniquely decodable codes. Des. Codes Cryptogr. 91, 3321–3330 (2023). https://doi.org/10.1007/s10623-023-01253-1
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DOI: https://doi.org/10.1007/s10623-023-01253-1