Structure of weighted projective Reed-Muller codes
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917361669373952 |
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| author | Nardi, Jade San-José, Rodrigo |
| author_facet | Nardi, Jade San-José, Rodrigo |
| contents | We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds on the generalized Hamming weights and to obtain a recursive construction for their subfield subcodes and their dual codes. The dual codes are further studied in more generality, where the recursive constructions may not apply, obtaining a description as an evaluation code when the degree is low. We also provide insights into the Schur products of these codes when they are not degenerate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24397 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Structure of weighted projective Reed-Muller codes Nardi, Jade San-José, Rodrigo Information Theory Commutative Algebra 94B05 (Primary) 11T71, 14G50 (Secondary) We provide a comprehensive overview of the fundamental structural properties of weighted projective Reed-Muller codes. We give a recursive construction for these codes, under some conditions for the weights, and we use it to derive bounds on the generalized Hamming weights and to obtain a recursive construction for their subfield subcodes and their dual codes. The dual codes are further studied in more generality, where the recursive constructions may not apply, obtaining a description as an evaluation code when the degree is low. We also provide insights into the Schur products of these codes when they are not degenerate. |
| title | Structure of weighted projective Reed-Muller codes |
| topic | Information Theory Commutative Algebra 94B05 (Primary) 11T71, 14G50 (Secondary) |
| url | https://arxiv.org/abs/2603.24397 |