Information on Result #1316167
Linear OA(12829, 392, F128, 17) (dual of [392, 363, 18]-code), using 7 step Varšamov–Edel lengthening with (ri) = (1, 6 times 0) based on linear OA(12828, 384, F128, 17) (dual of [384, 356, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(12828, 382, F128, 17) (dual of [382, 354, 18]-code), using an extension Ce(16) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(12826, 382, F128, 16) (dual of [382, 356, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(12829, 392, F128, 2, 17) (dual of [(392, 2), 755, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12829, 392, F128, 3, 17) (dual of [(392, 3), 1147, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(12829, 392, F128, 4, 17) (dual of [(392, 4), 1539, 18]-NRT-code) | [i] | ||
| 4 | Digital (12, 29, 392)-net over F128 | [i] | ||