Generalized Skew Multivariate Goppa Codes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909027824304128 |
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| author | Berardini, Elena Trivedi, Pranav |
| author_facet | Berardini, Elena Trivedi, Pranav |
| contents | We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain, as a particular case, the Generalized Skew Goppa codes. By providing a new parity check matrix for the latter, we show that, under some hypotheses, they are subfield subcodes of Generalized Skew Reed--Solomon codes. This result turns out to be helpful to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_06580 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized Skew Multivariate Goppa Codes Berardini, Elena Trivedi, Pranav Information Theory We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain, as a particular case, the Generalized Skew Goppa codes. By providing a new parity check matrix for the latter, we show that, under some hypotheses, they are subfield subcodes of Generalized Skew Reed--Solomon codes. This result turns out to be helpful to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance. |
| title | Generalized Skew Multivariate Goppa Codes |
| topic | Information Theory |
| url | https://arxiv.org/abs/2605.06580 |