Information on Result #1316155
Linear OA(12820, 590, F128, 11) (dual of [590, 570, 12]-code), using 204 step Varšamov–Edel lengthening with (ri) = (1, 16 times 0, 1, 186 times 0) based on linear OA(12818, 384, F128, 11) (dual of [384, 366, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12818, 382, F128, 11) (dual of [382, 364, 12]-code), using an extension Ce(10) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12816, 382, F128, 10) (dual of [382, 366, 11]-code), using an extension Ce(9) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 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(12820, 590, F128, 2, 11) (dual of [(590, 2), 1160, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12820, 590, F128, 3, 11) (dual of [(590, 3), 1750, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(12820, 590, F128, 4, 11) (dual of [(590, 4), 2340, 12]-NRT-code) | [i] | ||
| 4 | Digital (9, 20, 590)-net over F128 | [i] | ||