Generalized Hyperderivative Reed-Solomon Codes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911342586232832 |
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| author | Can, Mahir Bilen Horowitz, Benjamin |
| author_facet | Can, Mahir Bilen Horowitz, Benjamin |
| contents | This article introduces Generalized Hyperderivative Reed-Solomon codes (GHRS codes), which generalize NRT Reed-Solomon codes. Its main results are as follows: 1) every GHRS code is MDS, 2) the dual of a GHRS code is also an GHRS code, 3) determine subfamilies of GHRS codes whose members are low-density parity-check codes (LDPCs), and 4) determine a family of GHRS codes whose members are quasi-cyclic. We point out that there are GHRS codes having all of these properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Hyperderivative Reed-Solomon Codes Can, Mahir Bilen Horowitz, Benjamin Information Theory Rings and Algebras This article introduces Generalized Hyperderivative Reed-Solomon codes (GHRS codes), which generalize NRT Reed-Solomon codes. Its main results are as follows: 1) every GHRS code is MDS, 2) the dual of a GHRS code is also an GHRS code, 3) determine subfamilies of GHRS codes whose members are low-density parity-check codes (LDPCs), and 4) determine a family of GHRS codes whose members are quasi-cyclic. We point out that there are GHRS codes having all of these properties. |
| title | Generalized Hyperderivative Reed-Solomon Codes |
| topic | Information Theory Rings and Algebras |
| url | https://arxiv.org/abs/2512.22948 |