Information on Result #1316175
Linear OA(12837, 388, F128, 22) (dual of [388, 351, 23]-code), using 4 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0) based on linear OA(12836, 383, F128, 22) (dual of [383, 347, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(12836, 382, F128, 22) (dual of [382, 346, 23]-code), using an extension Ce(21) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12835, 382, F128, 21) (dual of [382, 347, 22]-code), using an extension Ce(20) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(12837, 388, F128, 2, 22) (dual of [(388, 2), 739, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12837, 388, F128, 3, 22) (dual of [(388, 3), 1127, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(12837, 388, F128, 4, 22) (dual of [(388, 4), 1515, 23]-NRT-code) | [i] | ||
| 4 | Digital (15, 37, 388)-net over F128 | [i] | ||