Sequence reconstruction for deletions
A code is (l, N)-reconstructible if for all pairs of codewords in a code, the number of distinct subsequences of length l is at most N - 1. In this work, we consider the sequence reconstruction problem introduced by Levenshtein. In particular, we study the reconstruction properties of 2-dimensional...
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| Format: | Final Year Project |
| Language: | English |
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Nanyang Technological University
2023
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| Online Access: | https://hdl.handle.net/10356/166487 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | A code is (l, N)-reconstructible if for all pairs of codewords in a code, the number of distinct subsequences of length l is at most N - 1. In this work, we consider the sequence reconstruction problem introduced by Levenshtein. In particular, we study the reconstruction properties of 2-dimensional Reed-Solomon codes in the construction given by Con et al., which gives 2-dimensional Reed-Solomon codes that are (3,1)-reconstructible in a field of size O(n^4). We then provide a less restrictive condition for construction that gives us Reed-Solomon codes that are (3,11)-reconstructible, (4,5)-reconstructible, (5,1)-reconstructible, but are available in field sizes that are much smaller. |
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