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The Modular Subset-Sum Problem and the size of deletion correcting codes

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Abstract

In this paper, using some results on the deletion correcting codes, we give an equivalent form of the Modular Subset-Sum Problem which is of significant importance in computer science and (quantum) cryptography. We also, using Ramanujan sums and their properties, give an explicit formula for the size of the Levenshtein code which has found many interesting applications, for examples, in studying DNA-based data storage and distributed message synchronization.

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Acknowledgements

The authors would like to thank the editor and the referees for carefully reading the paper, and for their useful comments which helped improve the paper.

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Miami University, Oxford, OH, 45056, USA

    Khodakhast Bibak

  2. Cyber Science Lab, School of Computer Science, University of Guelph, Guelph, ON, N1G 2W1, Canada

    Behrouz Zolfaghari

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  1. Khodakhast Bibak
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  2. Behrouz Zolfaghari
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Correspondence to Khodakhast Bibak.

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Communicated by T. Helleseth.

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Bibak, K., Zolfaghari, B. The Modular Subset-Sum Problem and the size of deletion correcting codes. Des. Codes Cryptogr. 90, 1721–1734 (2022). https://doi.org/10.1007/s10623-022-01073-9

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