Information on Result #1316174
Linear OA(12836, 420, F128, 21) (dual of [420, 384, 22]-code), using 34 step Varšamov–Edel lengthening with (ri) = (1, 33 times 0) based on linear OA(12835, 385, F128, 21) (dual of [385, 350, 22]-code), using
- construction XX applied to C1 = C([380,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([380,19]) [i] based on
- linear OA(12833, 381, F128, 20) (dual of [381, 348, 21]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12833, 381, F128, 20) (dual of [381, 348, 21]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12835, 381, F128, 21) (dual of [381, 346, 22]-code), using the BCH-code C(I) with length 381 | 1282−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12831, 381, F128, 19) (dual of [381, 350, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 381 | 1282−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(12836, 420, F128, 2, 21) (dual of [(420, 2), 804, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12836, 420, F128, 3, 21) (dual of [(420, 3), 1224, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(12836, 420, F128, 4, 21) (dual of [(420, 4), 1644, 22]-NRT-code) | [i] | ||
| 4 | Digital (15, 36, 420)-net over F128 | [i] | ||