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Uniform Sampling of Linear Codes with Prescribed Hull Dimension

  • Keita Ishizuka
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Abstract

We give exactly uniform samplers for linear codes with prescribed hull dimension, for the Euclidean, Hermitian, and symplectic inner products and over finite fields of every characteristic. Except for the Euclidean form over fields of odd characteristic, these are the first uniform samplers for arbitrary prescribed hull dimension. Each sample costs an expected O(k2 N + k log q) field operations for codes of dimension k in a space of dimension N over 𝔽q or 𝔽q2.

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Cite

BibTeXRIS
BibTeX
@misc{ishizuka2026uniform,
  title = {{Uniform Sampling of Linear Codes with Prescribed Hull Dimension}},
  author = {Keita Ishizuka},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.03578},
  eprint = {2611.03578},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.03578},
}
RIS
TY  - UNPB
TI  - Uniform Sampling of Linear Codes with Prescribed Hull Dimension
AU  - Keita Ishizuka
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.03578
UR  - https://arxiv.org/abs/2611.03578
AB  - We give exactly uniform samplers for linear codes with prescribed hull dimension, for the Euclidean, Hermitian, and symplectic inner products and over finite fields of every characteristic. Except for the Euclidean form over fields of odd characteristic, these are the first uniform samplers for arbitrary prescribed hull dimension. Each sample costs an expected O(k^2 N + k log q) field operations for codes of dimension k in a space of dimension N over 𝔽_q or 𝔽_q^2.
ER  -