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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Nanyang Technological University
2023
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sg-ntu-dr.10356-1664872023-05-08T15:38:46Z Sequence reconstruction for deletions Soh, Anna Li Lin Kiah Han Mao School of Physical and Mathematical Sciences HMKiah@ntu.edu.sg Science::Mathematics 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. Bachelor of Science in Mathematical Sciences 2023-05-02T04:44:25Z 2023-05-02T04:44:25Z 2023 Final Year Project (FYP) Soh, A. L. L. (2023). Sequence reconstruction for deletions. Final Year Project (FYP), Nanyang Technological University, Singapore. https://hdl.handle.net/10356/166487 https://hdl.handle.net/10356/166487 en application/pdf Nanyang Technological University |
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Science::Mathematics Soh, Anna Li Lin Sequence reconstruction for deletions |
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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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Kiah Han Mao |
| author_facet |
Kiah Han Mao Soh, Anna Li Lin |
| format |
Final Year Project |
| author |
Soh, Anna Li Lin |
| author_sort |
Soh, Anna Li Lin |
| title |
Sequence reconstruction for deletions |
| title_short |
Sequence reconstruction for deletions |
| title_full |
Sequence reconstruction for deletions |
| title_fullStr |
Sequence reconstruction for deletions |
| title_full_unstemmed |
Sequence reconstruction for deletions |
| title_sort |
sequence reconstruction for deletions |
| publisher |
Nanyang Technological University |
| publishDate |
2023 |
| url |
https://hdl.handle.net/10356/166487 |
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1770564491091640320 |