The weights in MDS codes
The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses t...
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sg-ntu-dr.10356-1003702023-02-28T19:42:16Z The weights in MDS codes Ezerman, Martianus Frederic Grassl, Markus Sole, Patrick School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Covering Radius MDS Codes The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version 2019-06-06T03:25:02Z 2019-12-06T20:21:20Z 2019-06-06T03:25:02Z 2019-12-06T20:21:20Z 2010 Journal Article Ezerman, M. F., Grassl, M., & Sole, P. (2011). The weights in MDS codes. IEEE Transactions on Information Theory, 57(1), 392-396. doi:10.1109/TIT.2010.2090246 0018-9448 https://hdl.handle.net/10356/100370 http://hdl.handle.net/10220/48554 10.1109/TIT.2010.2090246 en IEEE Transactions on Information Theory © 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The published version is available at: https://doi.org/10.1109/TIT.2010.2090246 5 p. application/pdf |
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DRNTU::Science::Mathematics Covering Radius MDS Codes Ezerman, Martianus Frederic Grassl, Markus Sole, Patrick The weights in MDS codes |
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The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Ezerman, Martianus Frederic Grassl, Markus Sole, Patrick |
| format |
Article |
| author |
Ezerman, Martianus Frederic Grassl, Markus Sole, Patrick |
| author_sort |
Ezerman, Martianus Frederic |
| title |
The weights in MDS codes |
| title_short |
The weights in MDS codes |
| title_full |
The weights in MDS codes |
| title_fullStr |
The weights in MDS codes |
| title_full_unstemmed |
The weights in MDS codes |
| title_sort |
weights in mds codes |
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2019 |
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https://hdl.handle.net/10356/100370 http://hdl.handle.net/10220/48554 |
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1759853028117053440 |