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PreprintCC0arXiv

Linear Equivalence of Full Weight Spectrum Cyclic Orbit Codes

  • Minjia Shi
  • Ferruh Ozbudak
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Abstract

We determine the linear-equivalence classes within the two families of full weight spectrum one-orbit cyclic subspace codes. This solves the second open problem posed by Castello, Polverino and Zullo [J. Combin. Theory Ser. A 212 (2025) 106005]. For the first family, the criterion is a fractional linear transformation over Fq followed by a power of q-Frobenius. For the second family, it is an affine transformation over Fq2 together with a power of q-Frobenius. We use polynomial spaces over finite fields, the linear-isometry theorem for cyclic orbit codes, and trace duality. The arguments include parameters belonging to proper subfields of the ambient field.

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Cite

BibTeXRIS
BibTeX
@misc{shi2026linear,
  title = {{Linear Equivalence of Full Weight Spectrum Cyclic Orbit Codes}},
  author = {Minjia Shi and Ferruh Ozbudak},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.04947},
  eprint = {2611.04947},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.04947},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Linear Equivalence of Full Weight Spectrum Cyclic Orbit Codes
AU  - Minjia Shi
AU  - Ferruh Ozbudak
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.04947
UR  - https://arxiv.org/abs/2611.04947
AB  - We determine the linear-equivalence classes within the two families of full weight spectrum one-orbit cyclic subspace codes. This solves the second open problem posed by Castello, Polverino and Zullo [J. Combin. Theory Ser. A 212 (2025) 106005]. For the first family, the criterion is a fractional linear transformation over F_q followed by a power of q-Frobenius. For the second family, it is an affine transformation over F_q^2 together with a power of q-Frobenius. We use polynomial spaces over finite fields, the linear-isometry theorem for cyclic orbit codes, and trace duality. The arguments include parameters belonging to proper subfields of the ambient field.
ER  -