Skew cyclic codes over F4R
This paper considers a new alphabet set, which is a ring that we call 4R, to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebrai...
| Main Authors: | , , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/146375 |
| _version_ | 1826115840381026304 |
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| author | Benbelkacem, Nasreddin Ezerman, Martianus Frederic Abualrub, Taher Aydin, Nuh Batoul, Aicha |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Benbelkacem, Nasreddin Ezerman, Martianus Frederic Abualrub, Taher Aydin, Nuh Batoul, Aicha |
| author_sort | Benbelkacem, Nasreddin |
| collection | NTU |
| description | This paper considers a new alphabet set, which is a ring that we call 4R, to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize 4R-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over 4 are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of R-skew cyclic codes which are reversible complement. |
| first_indexed | 2024-10-01T04:01:42Z |
| format | Journal Article |
| id | ntu-10356/146375 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:01:42Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1463752023-02-28T19:53:19Z Skew cyclic codes over F4R Benbelkacem, Nasreddin Ezerman, Martianus Frederic Abualrub, Taher Aydin, Nuh Batoul, Aicha School of Physical and Mathematical Sciences Science::Mathematics Linear Codes Skew Cyclic Codes This paper considers a new alphabet set, which is a ring that we call 4R, to construct linear error-control codes. Skew cyclic codes over this ring are then investigated in details. We define a nondegenerate inner product and provide a criteria to test for self-orthogonality. Results on the algebraic structures lead us to characterize 4R-skew cyclic codes. Interesting connections between the image of such codes under the Gray map to linear cyclic and skew-cyclic codes over 4 are shown. These allow us to learn about the relative dimension and distance profile of the resulting codes. Our setup provides a natural connection to DNA codes where additional biomolecular constraints must be incorporated into the design. We present a characterization of R-skew cyclic codes which are reversible complement. Accepted version 2021-02-15T02:55:57Z 2021-02-15T02:55:57Z 2020 Journal Article Benbelkacem, N., Ezerman, M. F., Abualrub, T., Aydin, N., & Batoul, A. (2020). Skew cyclic codes over F4R. Journal of Algebra and its Applications, 2250065-. doi:10.1142/S0219498822500657 1793-6829 https://hdl.handle.net/10356/146375 10.1142/S0219498822500657 2-s2.0-85098857100 2250065 en Journal of Algebra and its Applications Electronic version of an article published as Journal of Algebra and its Applications, 2250065-. https://doi.org/10.1142/S0219498822500657 @ copyright World Scientific Publishing Company [https://www.worldscientific.com/worldscinet/jaa]. application/pdf |
| spellingShingle | Science::Mathematics Linear Codes Skew Cyclic Codes Benbelkacem, Nasreddin Ezerman, Martianus Frederic Abualrub, Taher Aydin, Nuh Batoul, Aicha Skew cyclic codes over F4R |
| title | Skew cyclic codes over F4R |
| title_full | Skew cyclic codes over F4R |
| title_fullStr | Skew cyclic codes over F4R |
| title_full_unstemmed | Skew cyclic codes over F4R |
| title_short | Skew cyclic codes over F4R |
| title_sort | skew cyclic codes over f4r |
| topic | Science::Mathematics Linear Codes Skew Cyclic Codes |
| url | https://hdl.handle.net/10356/146375 |
| work_keys_str_mv | AT benbelkacemnasreddin skewcycliccodesoverf4r AT ezermanmartianusfrederic skewcycliccodesoverf4r AT abualrubtaher skewcycliccodesoverf4r AT aydinnuh skewcycliccodesoverf4r AT batoulaicha skewcycliccodesoverf4r |