Spectrum of Sizes for Perfect Deletion-Correcting Codes

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 Levenshtein 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. Key words. deletion-correcting codes, directed packings, group divisible designs, optimal codes, perfect codes AMS subject classifications. 94B25, 94B60, 05B05 DOI. 10.1137/090751311

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Yeow Meng Chee, Gennian Ge, Alan C. H. Ling
• Keywords: CORR 2010, Education, Perfect T-deletion-correcting Code, Possible Sizes, Q-ary 1-deletion-correcting Codes