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PreprintCC BY-SA 4.0HAL

Generalized Skew Multivariate Goppa Codes

  • Elena Berardini
  • Pranav Trivedi
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Abstract

We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain Generalized Skew Goppa codes as a special case. By providing a new parity-check matrix for the latter, we show that they are subfield subcodes of duals of Generalized Skew Reed--Solomon codes, up to the inverse field automorphism. This result is then used to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance.

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Cite

BibTeXRIS
BibTeX
@misc{berardini2026generalized,
  title = {{Generalized Skew Multivariate Goppa Codes}},
  author = {Elena Berardini and Pranav Trivedi},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2605.06580},
  eprint = {2605.06580},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05766836v1},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Generalized Skew Multivariate Goppa Codes
AU  - Elena Berardini
AU  - Pranav Trivedi
PY  - 2026
DA  - 2026/09/28
PB  - HAL
DO  - 10.48550/arxiv.2605.06580
UR  - https://hal.science/hal-05766836v1
AB  - We introduce Generalized Skew Multivariate Goppa codes relying on the theory of multivariate Ore polynomials. These codes contain Generalized Skew Goppa codes as a special case. By providing a new parity-check matrix for the latter, we show that they are subfield subcodes of duals of Generalized Skew Reed--Solomon codes, up to the inverse field automorphism. This result is then used to study the parameters of Skew Multivariate Goppa codes, for which we provide bounds on their dimension and minimum distance.
ER  -