Existence of Perfect 3-Deletion-Correcting Codes |
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Authors: | A. Mahmoodi |
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Affiliation: | (1) 1120 Finch Avenue West, 8th Floor, North York, Ontario, M3J 3H7, Canada. |
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Abstract: | Bours [4] recently showed some constructions for perfect 2 and 3-deletion-correcting codes from combinatorial designs. He settled existence of perfect 2-deletion-correcting codes with words of length 4. However, the existence of perfect 3-deletion-correcting codes with words of length 5, or T*(2, 5, v), remained unsettled for v 7, 8 (mod 10) and v = 13, 14, 15, 16. In this paper we provide new constructions for these codes from combinatorial designs, and show that a T*(2, 5, v) exists for all v. |
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Keywords: | code deletion-correcting perfect directed design BGDD DBIBD |
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