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...
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| المؤلفون الرئيسيون: | , , , , |
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| مؤلفون آخرون: | |
| التنسيق: | مقال |
| اللغة: | English |
| منشور في: |
2021
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| الموضوعات: | |
| الوصول للمادة أونلاين: | https://hdl.handle.net/10356/146375 |
| الوسوم: |
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| الملخص: | 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. |
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