Information on Result #730445

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]) based on
  1. 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]
  2. 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]
  3. 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]
  4. 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]
  5. linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code) (see above)

Mode: Constructive and 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:

ResultThis
result
only		Method
1Linear OA(12852, 16771, F128, 19) (dual of [16771, 16719, 20]-code) [i](u, u+v)-Construction
2Linear OA(12853, 16775, F128, 19) (dual of [16775, 16722, 20]-code) [i]
3Linear OA(12870, 2097540, F128, 19) (dual of [2097540, 2097470, 20]-code) [i]
4Linear OA(12871, 2097545, F128, 19) (dual of [2097545, 2097474, 20]-code) [i]
5Linear OA(12850, 16771, F128, 18) (dual of [16771, 16721, 19]-code) [i]
6Linear OA(12851, 16774, F128, 18) (dual of [16774, 16723, 19]-code) [i]
7Linear OA(12867, 2097540, F128, 18) (dual of [2097540, 2097473, 19]-code) [i]
8Linear OA(12868, 2097544, F128, 18) (dual of [2097544, 2097476, 19]-code) [i]
9Linear OOA(12815, 385, F128, 2, 9) (dual of [(385, 2), 755, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
10Linear OOA(12815, 385, F128, 3, 9) (dual of [(385, 3), 1140, 10]-NRT-code) [i]
11Linear OOA(12815, 385, F128, 4, 9) (dual of [(385, 4), 1525, 10]-NRT-code) [i]
12Digital (6, 15, 385)-net over F128 [i]
13Linear OA(12816, 497, F128, 9) (dual of [497, 481, 10]-code) [i]VarÅ¡amov–Edel Lengthening