Constructions and bounds on linear error-block codes
We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over . We also study the asymptotic of linear er...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
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2013
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| Online Access: | https://hdl.handle.net/10356/96410 http://hdl.handle.net/10220/9851 |
| _version_ | 1826119010674016256 |
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| author | Ling, San Özbudak, Ferruh |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ling, San Özbudak, Ferruh |
| author_sort | Ling, San |
| collection | NTU |
| description | We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over . We also study the asymptotic of linear error-block codes. We define the real valued function α q,m,a (δ), which is an analog of the important real valued function α q (δ) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert–Varshamov and algebraic geometry type lower bounds on α q,m,a (δ). We compare these lower bounds in graphs. |
| first_indexed | 2024-10-01T04:53:02Z |
| format | Journal Article |
| id | ntu-10356/96410 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:53:02Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/964102023-02-28T19:40:18Z Constructions and bounds on linear error-block codes Ling, San Özbudak, Ferruh School of Physical and Mathematical Sciences DRNTU::Science::Mathematics::Discrete mathematics::Cryptography We obtain new bounds on the parameters and we give new constructions of linear error-block codes. We obtain a Gilbert–Varshamov type construction. Using our bounds and constructions we obtain some infinite families of optimal linear error-block codes over . We also study the asymptotic of linear error-block codes. We define the real valued function α q,m,a (δ), which is an analog of the important real valued function α q (δ) in the asymptotic theory of classical linear error-correcting codes. We obtain both Gilbert–Varshamov and algebraic geometry type lower bounds on α q,m,a (δ). We compare these lower bounds in graphs. Accepted version 2013-04-23T06:59:46Z 2019-12-06T19:30:15Z 2013-04-23T06:59:46Z 2019-12-06T19:30:15Z 2007 2007 Journal Article Ling, S., & Özbudak, F. (2007). Constructions and bounds on linear error-block codes. Designs, Codes and Cryptography, 45(3), 297-316. https://hdl.handle.net/10356/96410 http://hdl.handle.net/10220/9851 10.1007/s10623-007-9119-9 en Designs, codes and cryptography © 2007 Springer Science+Business Media. This is the author created version of a work that has been peer reviewed and accepted for publication by Designs, Codes and Cryptography, Springer Science+Business Media. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1007/s10623-007-9119-9]. application/pdf |
| spellingShingle | DRNTU::Science::Mathematics::Discrete mathematics::Cryptography Ling, San Özbudak, Ferruh Constructions and bounds on linear error-block codes |
| title | Constructions and bounds on linear error-block codes |
| title_full | Constructions and bounds on linear error-block codes |
| title_fullStr | Constructions and bounds on linear error-block codes |
| title_full_unstemmed | Constructions and bounds on linear error-block codes |
| title_short | Constructions and bounds on linear error-block codes |
| title_sort | constructions and bounds on linear error block codes |
| topic | DRNTU::Science::Mathematics::Discrete mathematics::Cryptography |
| url | https://hdl.handle.net/10356/96410 http://hdl.handle.net/10220/9851 |
| work_keys_str_mv | AT lingsan constructionsandboundsonlinearerrorblockcodes AT ozbudakferruh constructionsandboundsonlinearerrorblockcodes |