Information on Result #1316151
Linear OA(12816, 497, F128, 9) (dual of [497, 481, 10]-code), using 111 step Varšamov–Edel lengthening with (ri) = (1, 110 times 0) based on linear OA(12815, 385, F128, 9) (dual of [385, 370, 10]-code), using
- construction XX applied to C1 = C([380,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([380,7]) [i] based on
- linear OA(12813, 381, F128, 8) (dual of [381, 368, 9]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(12813, 381, F128, 8) (dual of [381, 368, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(12815, 381, F128, 9) (dual of [381, 366, 10]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(12811, 381, F128, 7) (dual of [381, 370, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code) (see above)
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(12816, 497, F128, 2, 9) (dual of [(497, 2), 978, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12816, 497, F128, 3, 9) (dual of [(497, 3), 1475, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(12816, 497, F128, 4, 9) (dual of [(497, 4), 1972, 10]-NRT-code) | [i] | ||
| 4 | Digital (7, 16, 497)-net over F128 | [i] | ||