Information on Result #1316171
Linear OA(12833, 445, F128, 19) (dual of [445, 412, 20]-code), using 60 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 57 times 0) based on linear OA(12831, 383, F128, 19) (dual of [383, 352, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(12831, 382, F128, 19) (dual of [382, 351, 20]-code), using an extension Ce(18) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12830, 382, F128, 18) (dual of [382, 352, 19]-code), using an extension Ce(17) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(12833, 445, F128, 2, 19) (dual of [(445, 2), 857, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12833, 445, F128, 3, 19) (dual of [(445, 3), 1302, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(12833, 445, F128, 4, 19) (dual of [(445, 4), 1747, 20]-NRT-code) | [i] | ||
| 4 | Digital (14, 33, 445)-net over F128 | [i] | ||