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PreprintCC BY 4.0arXiv

Enumeration and Monotonicity of Linear Codes with Prescribed Hull Dimensions

  • Stefka Bouyuklieva
  • Iliya Bouyukliev
  • Keita Ishizuka
  • Ferruh Özbudak
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Abstract

The hull of a linear code is the intersection of the code with its dual and depends on the choice of inner product. We study how the numbers of linear codes with prescribed Euclidean, Hermitian, and symplectic hull dimensions vary with the hull dimension. Building on closed enumeration formulae, we derive exact ratio decompositions for the Hermitian and symplectic cases, determine the parameter ranges in which monotonicity holds, and identify the exceptional families. We also compare the three inner products and complement the theoretical analysis with computational classification results for quaternary codes.

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Cite

BibTeXRIS
BibTeX
@misc{bouyuklieva2026enumeration,
  title = {{Enumeration and Monotonicity of Linear Codes with Prescribed Hull Dimensions}},
  author = {Stefka Bouyuklieva and Iliya Bouyukliev and Keita Ishizuka and Ferruh Özbudak},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.29204},
  eprint = {2605.29204},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.29204},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Enumeration and Monotonicity of Linear Codes with Prescribed Hull Dimensions
AU  - Stefka Bouyuklieva
AU  - Iliya Bouyukliev
AU  - Keita Ishizuka
AU  - Ferruh Özbudak
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2605.29204
UR  - https://arxiv.org/abs/2605.29204
AB  - The hull of a linear code is the intersection of the code with its dual and depends on the choice of inner product. We study how the numbers of linear codes with prescribed Euclidean, Hermitian, and symplectic hull dimensions vary with the hull dimension. Building on closed enumeration formulae, we derive exact ratio decompositions for the Hermitian and symplectic cases, determine the parameter ranges in which monotonicity holds, and identify the exceptional families. We also compare the three inner products and complement the theoretical analysis with computational classification results for quaternary codes.
ER  -