Spectrum of Sizes for Perfect Deletion-Correcting Codes
Information Theory
2010-08-10 v1 Discrete Mathematics
Combinatorics
math.IT
Abstract
One peculiarity with deletion-correcting codes is that perfect -deletion-correcting codes of the same length over the same alphabet can have different numbers of codewords, because the balls of radius with respect to the Levenshte\u{\i}n distance may be of different sizes. There is interest, therefore, in determining all possible sizes of a perfect -deletion-correcting code, given the length and the alphabet size~. In this paper, we determine completely the spectrum of possible sizes for perfect -ary 1-deletion-correcting codes of length three for all , and perfect -ary 2-deletion-correcting codes of length four for almost all , leaving only a small finite number of cases in doubt.
Cite
@article{arxiv.1008.1343,
title = {Spectrum of Sizes for Perfect Deletion-Correcting Codes},
author = {Yeow Meng Chee and Gennian Ge and Alan C. H. Ling},
journal= {arXiv preprint arXiv:1008.1343},
year = {2010}
}
Comments
23 pages