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arXiv · 1008.1343

Spectrum of Sizes for Perfect Deletion-Correcting Codes

Yeow Meng Chee·Gennian Ge·Alan C. H. Ling
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Abstract

One peculiarity with deletion-correcting codes is that perfect $t$-deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius $t$ with respect to the Levenshte\uın distance may be of different sizes. There is interest, therefore, in determining all possible sizes of a perfect $t$-deletion-correcting code, given the length $n$ and the alphabet size~$q$. In this paper, we determine completely the spectrum of possible sizes for perfect $q$-ary 1-deletion-correcting codes of length three for all $q$, and perfect $q$-ary 2-deletion-correcting codes of length four for almost all $q$, leaving only a small finite number of cases in doubt.

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Yeow Meng Chee, Gennian Ge, Alan C. H. Ling. 2010-08-07. Spectrum of Sizes for Perfect Deletion-Correcting Codes. https://doi.org/10.1137/090751311

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