Generalized Reed-Muller codes: A new construction of information sets
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911767657971712 |
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| author | Bernal, José Joaquín |
| author_facet | Bernal, José Joaquín |
| contents | In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see that for first-order codes the result for binary Reed-Muller codes is also valid, while for second-order codes, with q > 2, we have to manage more complex defining sets and we show that we get different information sets. We also present some examples and associated open problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16911 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized Reed-Muller codes: A new construction of information sets Bernal, José Joaquín Information Theory In [2] we show how to construct information sets for Reed-Muller codes only in terms of their basic parameters. In this work we deal with the corresponding problem for q-ary Generalized Reed-Muller codes of first and second order. We see that for first-order codes the result for binary Reed-Muller codes is also valid, while for second-order codes, with q > 2, we have to manage more complex defining sets and we show that we get different information sets. We also present some examples and associated open problems. |
| title | Generalized Reed-Muller codes: A new construction of information sets |
| topic | Information Theory |
| url | https://arxiv.org/abs/2401.16911 |