Information on Result #1316147
Linear OA(12812, 433, F128, 7) (dual of [433, 421, 8]-code), using 49 step Varšamov–Edel lengthening with (ri) = (1, 48 times 0) based on linear OA(12811, 383, F128, 7) (dual of [383, 372, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(12811, 382, F128, 7) (dual of [382, 371, 8]-code), using an extension Ce(6) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(12810, 382, F128, 6) (dual of [382, 372, 7]-code), using an extension Ce(5) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(1280, 1, F128, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 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(12812, 433, F128, 2, 7) (dual of [(433, 2), 854, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12812, 433, F128, 3, 7) (dual of [(433, 3), 1287, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12812, 433, F128, 4, 7) (dual of [(433, 4), 1720, 8]-NRT-code) | [i] | ||
| 4 | Digital (5, 12, 433)-net over F128 | [i] | ||