Information on Result #1316153
Linear OA(12818, 542, F128, 10) (dual of [542, 524, 11]-code), using 157 step Varšamov–Edel lengthening with (ri) = (1, 5 times 0, 1, 150 times 0) based on linear OA(12816, 383, F128, 10) (dual of [383, 367, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(12815, 382, F128, 9) (dual of [382, 367, 10]-code), using an extension Ce(8) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(12818, 542, F128, 2, 10) (dual of [(542, 2), 1066, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12818, 542, F128, 3, 10) (dual of [(542, 3), 1608, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(12818, 542, F128, 4, 10) (dual of [(542, 4), 2150, 11]-NRT-code) | [i] | ||
| 4 | Digital (8, 18, 542)-net over F128 | [i] | ||