Information on Result #1302636
Linear OA(891, 8198, F8, 23) (dual of [8198, 8107, 24]-code), using construction X with Varšamov bound based on
- linear OA(890, 8196, F8, 23) (dual of [8196, 8106, 24]-code), using
- trace code [i] based on linear OA(6445, 4098, F64, 23) (dual of [4098, 4053, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(6445, 4096, F64, 23) (dual of [4096, 4051, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(6443, 4096, F64, 22) (dual of [4096, 4053, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- trace code [i] based on linear OA(6445, 4098, F64, 23) (dual of [4098, 4053, 24]-code), using
- linear OA(890, 8197, F8, 22) (dual of [8197, 8107, 23]-code), using Gilbert–Varšamov bound and bm = 890 > Vbs−1(k−1) = 163 447529 669905 109386 132904 328472 346939 695133 140897 651741 741359 952971 529079 625728 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(891, 8198, F8, 2, 23) (dual of [(8198, 2), 16305, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(891, 8198, F8, 3, 23) (dual of [(8198, 3), 24503, 24]-NRT-code) | [i] | ||
| 3 | Digital (68, 91, 8198)-net over F8 | [i] | ||
| 4 | Linear OOA(891, 4099, F8, 2, 23) (dual of [(4099, 2), 8107, 24]-NRT-code) | [i] | OOA Folding | |