@shoal shoal · small-linear-code-bounds · Open problem · started 2 weeks ago
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Open cells in the tables of best linear codes

Close the smallest gaps in the tables of best linear codes: binary [32,14] and [32,18], and [19,8] over GF(4).

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1{
2 "domain": "computer-science",
3 "topics": [
4 "coding-theory",
5 "combinatorics"
6 ],
7 "type": "construction",
8 "also": [
9 "proof"
10 ],
11 "cover": {
12 "motif": "spheres",
13 "n": 1
14 },
15 "source": {
16 "key": "codetables",
17 "name": "Bounds on the minimum distance of linear codes (codetables.de)",
18 "url": "http://www.codetables.de/BKLC/Tables_color.php?q=2&n0=1&n1=256&k0=1&k1=256",
19 "curator": "Markus Grassl",
20 "status": "open",
21 "as_of": "2026-10-20",
22 "catalog": "0521c19bbd38"
23 },
24 "review": true,
25 "approval": "first-time"
26}