Linear codes over F4R and their MacWilliams identity
Let 4 be the field of four elements. We denote by R the commutative ring, with 16 elements, 4 v4:= {a vb|a,b 4} with v2 = v. This work defines linear codes over the ring of mixed alphabets 4R as well as their dual codes under a nondegenerate inner product. We then derive the systematic form of the r...
Saved in:
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2021
|
| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/146385 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Nanyang Technological University |
| Language: | English |
| id |
sg-ntu-dr.10356-146385 |
|---|---|
| record_format |
dspace |
| spelling |
sg-ntu-dr.10356-1463852023-02-28T19:53:07Z Linear codes over F4R and their MacWilliams identity Benbelkacem, Nasreddine Ezerman, Martianus Frederic Abualrub, Taher School of Physical and Mathematical Sciences Science::Mathematics::Algebra Code Over Ring Mixed Alphabets Let 4 be the field of four elements. We denote by R the commutative ring, with 16 elements, 4 v4:= {a vb|a,b 4} with v2 = v. This work defines linear codes over the ring of mixed alphabets 4R as well as their dual codes under a nondegenerate inner product. We then derive the systematic form of the respective generator matrices of the codes and their dual codes. We wrap the paper up by proving the MacWilliams identity for linear codes over 4R. Accepted version 2021-02-15T08:09:07Z 2021-02-15T08:09:07Z 2020 Journal Article Benbelkacem, N., Ezerman, M. F., & Abualrub, T. (2020). Linear codes over F4R and their MacWilliams identity. Discrete Mathematics, Algorithms and Applications, 12(6), 2050085-. doi:10.1142/S1793830920500858 1793-8317 https://hdl.handle.net/10356/146385 10.1142/S1793830920500858 2-s2.0-85095445446 6 12 2050085 en Discrete Mathematics, Algorithms and Applications Electronic version of an article published as Discrete Mathematics, Algorithms and Applications, 12(6), 2050085-. https://doi.org/10.1142/S1793830920500858 @ copyright World Scientific Publishing Company [https://www.worldscientific.com/worldscinet/dmaa]. application/pdf |
| institution |
Nanyang Technological University |
| building |
NTU Library |
| continent |
Asia |
| country |
Singapore Singapore |
| content_provider |
NTU Library |
| collection |
DR-NTU |
| language |
English |
| topic |
Science::Mathematics::Algebra Code Over Ring Mixed Alphabets |
| spellingShingle |
Science::Mathematics::Algebra Code Over Ring Mixed Alphabets Benbelkacem, Nasreddine Ezerman, Martianus Frederic Abualrub, Taher Linear codes over F4R and their MacWilliams identity |
| description |
Let 4 be the field of four elements. We denote by R the commutative ring, with 16 elements, 4 v4:= {a vb|a,b 4} with v2 = v. This work defines linear codes over the ring of mixed alphabets 4R as well as their dual codes under a nondegenerate inner product. We then derive the systematic form of the respective generator matrices of the codes and their dual codes. We wrap the paper up by proving the MacWilliams identity for linear codes over 4R. |
| author2 |
School of Physical and Mathematical Sciences |
| author_facet |
School of Physical and Mathematical Sciences Benbelkacem, Nasreddine Ezerman, Martianus Frederic Abualrub, Taher |
| format |
Article |
| author |
Benbelkacem, Nasreddine Ezerman, Martianus Frederic Abualrub, Taher |
| author_sort |
Benbelkacem, Nasreddine |
| title |
Linear codes over F4R and their MacWilliams identity |
| title_short |
Linear codes over F4R and their MacWilliams identity |
| title_full |
Linear codes over F4R and their MacWilliams identity |
| title_fullStr |
Linear codes over F4R and their MacWilliams identity |
| title_full_unstemmed |
Linear codes over F4R and their MacWilliams identity |
| title_sort |
linear codes over f4r and their macwilliams identity |
| publishDate |
2021 |
| url |
https://hdl.handle.net/10356/146385 |
| _version_ |
1759857500916547584 |