Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound
It was shown by Massey that linear complementary dual (LCD) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV) bound. Until now, the GV bound still remains to be the best asymptotical lower bound for LCD codes. In this paper, we show tha...
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2020
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| Online Access: | https://hdl.handle.net/10356/140042 |
| _version_ | 1811679376509501440 |
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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 | It was shown by Massey that linear complementary dual (LCD) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV) bound. Until now, the GV bound still remains to be the best asymptotical lower bound for LCD codes. In this paper, we show that an algebraic geometry code over a finite field of even characteristic is equivalent to an LCD code and consequently there exists a family of LCD codes that are equivalent to algebraic geometry codes and exceed the asymptotical GV bound. |
| first_indexed | 2024-10-01T03:08:10Z |
| format | Journal Article |
| id | ntu-10356/140042 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T03:08:10Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1400422020-05-26T05:32:08Z Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound Jin, Lingfei Xing, Chaoping School of Physical and Mathematical Sciences Science::Mathematics Linear Complementary Dual Codes Algebraic Geometry Codes It was shown by Massey that linear complementary dual (LCD) codes are asymptotically good. In 2004, Sendrier proved that LCD codes meet the asymptotic Gilbert-Varshamov (GV) bound. Until now, the GV bound still remains to be the best asymptotical lower bound for LCD codes. In this paper, we show that an algebraic geometry code over a finite field of even characteristic is equivalent to an LCD code and consequently there exists a family of LCD codes that are equivalent to algebraic geometry codes and exceed the asymptotical GV bound. MOE (Min. of Education, S’pore) 2020-05-26T05:32:08Z 2020-05-26T05:32:08Z 2017 Journal Article Jin, L., & Xing, C. (2018). Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound. IEEE Transactions on Information Theory, 64(9), 6277-6282. doi:10.1109/TIT.2017.2773057 0018-9448 https://hdl.handle.net/10356/140042 10.1109/TIT.2017.2773057 2-s2.0-85034251074 9 64 6277 6282 en IEEE Transactions on Information Theory © 2017 IEEE. All rights reserved. |
| spellingShingle | Science::Mathematics Linear Complementary Dual Codes Algebraic Geometry Codes Jin, Lingfei Xing, Chaoping Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title_full | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title_fullStr | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title_full_unstemmed | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title_short | Algebraic geometry codes with complementary duals exceed the asymptotic Gilbert-Varshamov bound |
| title_sort | algebraic geometry codes with complementary duals exceed the asymptotic gilbert varshamov bound |
| topic | Science::Mathematics Linear Complementary Dual Codes Algebraic Geometry Codes |
| url | https://hdl.handle.net/10356/140042 |
| work_keys_str_mv | AT jinlingfei algebraicgeometrycodeswithcomplementarydualsexceedtheasymptoticgilbertvarshamovbound AT xingchaoping algebraicgeometrycodeswithcomplementarydualsexceedtheasymptoticgilbertvarshamovbound |