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https://hdl.handle.net/10356/146385| Title: | Linear codes over F4R and their MacWilliams identity | Authors: | Benbelkacem, Nasreddine Ezerman, Martianus Frederic Abualrub, Taher |
Keywords: | Science::Mathematics::Algebra | Issue Date: | 2020 | Source: | 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 | Journal: | Discrete Mathematics, Algorithms and Applications | Abstract: | 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. | URI: | https://hdl.handle.net/10356/146385 | ISSN: | 1793-8317 | DOI: | 10.1142/S1793830920500858 | Schools: | School of Physical and Mathematical Sciences | Rights: | 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]. | Fulltext Permission: | open | Fulltext Availability: | With Fulltext |
| Appears in Collections: | SPMS Journal Articles |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| Linear codes over F4R and their MacWilliams identity.pdf | 366.68 kB | Adobe PDF |  View/Open |
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