New Binary Codes From Rational Function Fields
In this paper, we present an algebraic construction of binary codes through rational function fields. We make use of certain multiplicative group of rational functions for our construction. In particular, the point at infinity can be employed in our construction to get codes of length up to q+1, whe...
| Main Authors: | , |
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| Format: | Journal Article |
| Language: | English |
| Published: |
2015
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| Online Access: | https://hdl.handle.net/10356/81336 http://hdl.handle.net/10220/39227 |
| _version_ | 1826112970157981696 |
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| author | Jin, Lingfei Xing, Chaoping |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Jin, Lingfei Xing, Chaoping |
| author_sort | Jin, Lingfei |
| collection | NTU |
| description | In this paper, we present an algebraic construction of binary codes through rational function fields. We make use of certain multiplicative group of rational functions for our construction. In particular, the point at infinity can be employed in our construction to get codes of length up to q+1, where q is the ground field size. As a result, several new binary constant-weight codes are found and many new binary nonlinear codes are presented. |
| first_indexed | 2024-10-01T03:15:32Z |
| format | Journal Article |
| id | ntu-10356/81336 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:15:32Z |
| publishDate | 2015 |
| record_format | dspace |
| spelling | ntu-10356/813362023-02-28T19:30:47Z New Binary Codes From Rational Function Fields Jin, Lingfei Xing, Chaoping School of Physical and Mathematical Sciences Binary constant-weight codes Rational functions Point at infinity Multiplicative group Binary codes In this paper, we present an algebraic construction of binary codes through rational function fields. We make use of certain multiplicative group of rational functions for our construction. In particular, the point at infinity can be employed in our construction to get codes of length up to q+1, where q is the ground field size. As a result, several new binary constant-weight codes are found and many new binary nonlinear codes are presented. Accepted version 2015-12-29T02:10:36Z 2019-12-06T14:28:42Z 2015-12-29T02:10:36Z 2019-12-06T14:28:42Z 2014 Journal Article Jin, L., & Xing, C. (2015). New Binary Codes From Rational Function Fields. IEEE Transactions on Information Theory, 61(1), 60-65. 0018-9448 https://hdl.handle.net/10356/81336 http://hdl.handle.net/10220/39227 10.1109/TIT.2014.2352306 en IEEE Transactions on Information Theory © 2014 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: [http://dx.doi.org/10.1109/TIT.2014.2352306]. 10 p. application/pdf |
| spellingShingle | Binary constant-weight codes Rational functions Point at infinity Multiplicative group Binary codes Jin, Lingfei Xing, Chaoping New Binary Codes From Rational Function Fields |
| title | New Binary Codes From Rational Function Fields |
| title_full | New Binary Codes From Rational Function Fields |
| title_fullStr | New Binary Codes From Rational Function Fields |
| title_full_unstemmed | New Binary Codes From Rational Function Fields |
| title_short | New Binary Codes From Rational Function Fields |
| title_sort | new binary codes from rational function fields |
| topic | Binary constant-weight codes Rational functions Point at infinity Multiplicative group Binary codes |
| url | https://hdl.handle.net/10356/81336 http://hdl.handle.net/10220/39227 |
| work_keys_str_mv | AT jinlingfei newbinarycodesfromrationalfunctionfields AT xingchaoping newbinarycodesfromrationalfunctionfields |