A q-polynomial approach to cyclic codes
Cyclic codes have been an interesting topic of both mathematics and engineering for decades. They are prominently used in consumer electronics, data transmission technologies, broadcast systems, and computer applications. Three classical approaches to the study and construction of cyclic codes are t...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/106486 http://hdl.handle.net/10220/17985 http://dx.doi.org/10.1016/j.ffa.2012.12.005 |
| _version_ | 1826110401854570496 |
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| author | Ding, Cunsheng Ling, San |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Ding, Cunsheng Ling, San |
| author_sort | Ding, Cunsheng |
| collection | NTU |
| description | Cyclic codes have been an interesting topic of both mathematics and engineering for decades. They are prominently used in consumer electronics, data transmission technologies, broadcast systems, and computer applications. Three classical approaches to the study and construction of cyclic codes are those based on the generator matrix, the generator polynomial and the idempotent. The objective of this paper is to develop another approach – the q-polynomial approach. Fundamental theory of this approach will be developed, and will be employed to construct a new family of cyclic codes in this paper. |
| first_indexed | 2024-10-01T02:33:49Z |
| format | Journal Article |
| id | ntu-10356/106486 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:33:49Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | ntu-10356/1064862019-12-06T22:12:51Z A q-polynomial approach to cyclic codes Ding, Cunsheng Ling, San School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Cyclic codes have been an interesting topic of both mathematics and engineering for decades. They are prominently used in consumer electronics, data transmission technologies, broadcast systems, and computer applications. Three classical approaches to the study and construction of cyclic codes are those based on the generator matrix, the generator polynomial and the idempotent. The objective of this paper is to develop another approach – the q-polynomial approach. Fundamental theory of this approach will be developed, and will be employed to construct a new family of cyclic codes in this paper. 2013-12-02T08:26:26Z 2019-12-06T22:12:51Z 2013-12-02T08:26:26Z 2019-12-06T22:12:51Z 2013 2013 Journal Article Ding, C., & Ling, S. (2013). A q-polynomial approach to cyclic codes. Finite fields and their applications, 20, 1-14. 1071-5797 https://hdl.handle.net/10356/106486 http://hdl.handle.net/10220/17985 http://dx.doi.org/10.1016/j.ffa.2012.12.005 en Finite fields and their applications |
| spellingShingle | DRNTU::Science::Mathematics Ding, Cunsheng Ling, San A q-polynomial approach to cyclic codes |
| title | A q-polynomial approach to cyclic codes |
| title_full | A q-polynomial approach to cyclic codes |
| title_fullStr | A q-polynomial approach to cyclic codes |
| title_full_unstemmed | A q-polynomial approach to cyclic codes |
| title_short | A q-polynomial approach to cyclic codes |
| title_sort | q polynomial approach to cyclic codes |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/106486 http://hdl.handle.net/10220/17985 http://dx.doi.org/10.1016/j.ffa.2012.12.005 |
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