Information on Result #1324166
Linear OA(4236, 65606, F4, 37) (dual of [65606, 65370, 38]-code), using construction X with Varšamov bound based on
- linear OA(4231, 65598, F4, 37) (dual of [65598, 65367, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(414, 62, F4, 7) (dual of [62, 48, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- a “GraXX†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(414, 65, F4, 7) (dual of [65, 51, 8]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] based on
- linear OA(4231, 65601, F4, 34) (dual of [65601, 65370, 35]-code), using Gilbert–Varšamov bound and bm = 4231 > Vbs−1(k−1) = 576393 619794 147941 663561 559415 077776 725816 188588 348401 400757 724314 191987 233195 083172 830855 629364 321200 283395 628848 152583 918601 735583 513443 [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(4237, 65607, F4, 37) (dual of [65607, 65370, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4236, 32803, F4, 2, 37) (dual of [(32803, 2), 65370, 38]-NRT-code) | [i] | OOA Folding | |