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Applications of Gaussian Binomials to Coding Theory for Deletion Error Correction

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Abstract

We present new applications of q-binomials, also known as Gaussian binomial coefficients. Our main theorems determine cardinalities of certain error-correcting codes based on Varshamov–Tenengolts codes and prove a curious phenomenon relating to deletion spheres.

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Acknowledgements

This paper is partially supported by KAKENHI 16K12391, 18H01435, and 16K06336. The authors are grateful to Dr. Soichi Okada for bringing to our attention important related works.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-0022, Japan

    Manabu Hagiwara

  2. Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall (Keller Hall 401A), Honolulu, HI, 96822, USA

    Justin Kong

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  1. Manabu Hagiwara
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  2. Justin Kong
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Correspondence to Manabu Hagiwara.

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This paper is partially supported by KAKENHI 16K12391, 18H01435, and 16K06336.

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Hagiwara, M., Kong, J. Applications of Gaussian Binomials to Coding Theory for Deletion Error Correction. Ann. Comb. 24, 379–393 (2020). https://doi.org/10.1007/s00026-020-00494-4

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