Information on Result #1425012
Linear OOA(4165, 16445, F4, 2, 29) (dual of [(16445, 2), 32725, 30]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(4165, 16445, F4, 29) (dual of [16445, 16280, 30]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(4162, 16440, F4, 29) (dual of [16440, 16278, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(20) [i] based on
- linear OA(4148, 16384, F4, 29) (dual of [16384, 16236, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(414, 56, F4, 7) (dual of [56, 42, 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(28) ⊂ Ce(20) [i] based on
- linear OA(4162, 16442, F4, 27) (dual of [16442, 16280, 28]-code), using Gilbert–Varšamov bound and bm = 4162 > Vbs−1(k−1) = 254277 229678 767333 724530 915378 760991 998755 967322 095445 840310 441021 103141 720896 948748 295649 426400 [i]
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(4162, 16440, F4, 29) (dual of [16440, 16278, 30]-code), 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(4165, 8222, F4, 3, 29) (dual of [(8222, 3), 24501, 30]-NRT-code) | [i] | OOA Folding | |