Data & Software

Data behind my classification and construction papers is published under an open licence so the results can be reused and checked independently. Every record is archived on Zenodo with its own DOI.

3 datasets · 12 records · 368.5 GB

Classification of LCD codes over F₂, F₃ and F₄

Generator matrices of one representative of every equivalence class of linear complementary dual (LCD) codes: binary codes of length up to 19, ternary codes of length up to 15, and quaternary Hermitian LCD codes of length up to 13. Complete in each range.

FieldLengths coveredSize
F₂ Binary n ≤ 19 204.4 GB
F₃ Ternary n ≤ 15 141.5 GB
F₄ Quaternary Hermitian n ≤ 13 18.2 GB
Accompanies
Keita Ishizuka, Classification of binary, ternary and quaternary Hermitian LCD codes arXiv:2610.30561
Format
Plain-text generator matrices, xz-compressed, split into parts. Each record carries a README.md describing the full ten-record set.
License
CC-BY-4.0
Published
2026-10-19
Updated
2026-11-06: Binary part 1 replaced by version 1.1: the orders of the automorphism groups of two codes in q2_n19_k1 were corrected.

10 records · 364.1 GB · each DOI resolves to the latest version

Cite this dataset

Please cite the accompanying paper as well as this dataset.

@misc{ishizuka2026lcdclassification,
  author    = {Ishizuka, Keita},
  title     = {Classification of LCD codes over F2, F3 and F4},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23461336},
  url       = {https://doi.org/10.5281/zenodo.23461336},
  note      = {Dataset; 10 records, each with its own DOI}
}

Simple graphs with idempotent adjacency matrices over F₂ on at most 19 vertices

One representative of every isomorphism class of simple graphs on at most 19 vertices, with at least one edge, whose adjacency matrix A satisfies A² = A over F₂: 81,748,770 graphs in all. These graphs are exactly the orthogonal projectors of the binary even LCD codes, and two graphs are isomorphic precisely when the corresponding codes are permutation equivalent, so the data also classify every binary even LCD code of length at most 19. Each line carries the minimum distance of the code, the order of the automorphism group and the adjacency matrix. Completeness is certified by the mass formula for binary even LCD codes at every length and dimension.

VerticesDimensionsSize
n = 19 k = 2 – 18 4.2 GB
n = 18 k = 2 – 16 215.5 MB
n = 17 k = 2 – 16 14.6 MB
n = 16 k = 2 – 14 1.4 MB
n ≤ 15 k = 2 – 14 311 kB
Accompanies
Keita Ishizuka, Binary LCD Codes and Their Graph Representations arXiv:2407.07689
Format
Plain-text adjacency matrices, xz-compressed, one file per (vertices, dimension). Summary tables counts_nk.csv and stats_nkd.csv, plus README.md.
License
CC-BY-4.0
Published
2026-11-05

1 record · 4.4 GB · each DOI resolves to the latest version

Cite this dataset

Please cite the accompanying paper as well as this dataset.

@misc{ishizuka2026evenlcdgraphs,
  author    = {Ishizuka, Keita},
  title     = {Simple graphs with idempotent adjacency matrices over F2 on at most 19 vertices},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23988489},
  url       = {https://doi.org/10.5281/zenodo.23988489}
}

Construction data for binary LCD codes of codimension 8

Explicit binary LCD [n, n-8] codes for every n with 9 ≤ n ≤ 247, given as subsets S of F₂⁸ \ {0} whose parity-check matrix H_S satisfies det(H_S H_S^T) ≠ 0. These determine the largest minimum weight d(n, n-8) for all n. Includes a dependency-free Python script that re-verifies every stated property.

Accompanies
Keita Ishizuka, Yuhi Kamio, Caps and LCD Codes with Large Dimensions arXiv:2604.03734
Format
Plain text (codim8_sets.txt), verification script (verify.py), README.md.
License
CC-BY-4.0
Published
2026-10-22

1 record · 113 kB · each DOI resolves to the latest version

Cite this dataset

Please cite the accompanying paper as well as this dataset.

@misc{ishizuka2026codim8,
  author    = {Ishizuka, Keita and Kamio, Yuhi},
  title     = {Construction data for binary LCD codes of codimension 8},
  year      = {2026},
  publisher = {Zenodo},
  doi       = {10.5281/zenodo.23486096},
  url       = {https://doi.org/10.5281/zenodo.23486096}
}