Information on Result #1324260
Linear OA(4256, 65625, F4, 39) (dual of [65625, 65369, 40]-code), using construction X with Varšamov bound based on
- linear OA(4254, 65621, F4, 39) (dual of [65621, 65367, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(28) [i] based on
- linear OA(4233, 65536, F4, 39) (dual of [65536, 65303, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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(421, 85, F4, 9) (dual of [85, 64, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(421, 86, F4, 9) (dual of [86, 65, 10]-code), using
- construction X applied to Ce(38) ⊂ Ce(28) [i] based on
- linear OA(4254, 65623, F4, 38) (dual of [65623, 65369, 39]-code), using Gilbert–Varšamov bound and bm = 4254 > Vbs−1(k−1) = 551 128477 270919 975872 685226 900687 033324 704622 957405 442119 108540 795763 512551 542679 920272 944634 906718 520761 884688 495843 483102 444642 053340 345419 539778 294550 [i]
- linear OA(40, 2, F4, 0) (dual of [2, 2, 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(4256, 65625, F4, 2, 39) (dual of [(65625, 2), 130994, 40]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4256, 65625, F4, 3, 39) (dual of [(65625, 3), 196619, 40]-NRT-code) | [i] | ||
| 3 | Digital (217, 256, 65625)-net over F4 | [i] | ||
| 4 | Linear OOA(4256, 32812, F4, 2, 39) (dual of [(32812, 2), 65368, 40]-NRT-code) | [i] | OOA Folding | |