Information on Result #1324182
Linear OA(4237, 65613, F4, 36) (dual of [65613, 65376, 37]-code), using construction X with Varšamov bound based on
- linear OA(4236, 65611, F4, 36) (dual of [65611, 65375, 37]-code), using
- construction X applied to Ce(36) ⊂ Ce(26) [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(4161, 65536, F4, 27) (dual of [65536, 65375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(419, 75, F4, 8) (dual of [75, 56, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(419, 87, F4, 8) (dual of [87, 68, 9]-code), using
- construction X applied to Ce(36) ⊂ Ce(26) [i] based on
- linear OA(4236, 65612, F4, 35) (dual of [65612, 65376, 36]-code), using Gilbert–Varšamov bound and bm = 4236 > Vbs−1(k−1) = 3353 709460 062317 792299 695346 518390 798070 476522 898703 120640 354724 139081 200606 850116 574957 895895 960534 573410 112689 834377 534405 948953 574962 703470 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OOA(4237, 65613, F4, 2, 36) (dual of [(65613, 2), 130989, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4237, 65613, F4, 3, 36) (dual of [(65613, 3), 196602, 37]-NRT-code) | [i] | ||
| 3 | Digital (201, 237, 65613)-net over F4 | [i] | ||
| 4 | Linear OOA(4237, 32806, F4, 2, 36) (dual of [(32806, 2), 65375, 37]-NRT-code) | [i] | OOA Folding | |