Information on Result #1072078
Linear OOA(12812, 1048706, F128, 4, 4) (dual of [(1048706, 4), 4194812, 5]-NRT-code), using appending kth column based on linear OOA(12812, 1048706, F128, 3, 4) (dual of [(1048706, 3), 3146106, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(1282, 129, F128, 3, 2) (dual of [(129, 3), 385, 3]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;385,128) [i]
- linear OOA(12810, 1048577, F128, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- linear OOA(1282, 129, F128, 3, 2) (dual of [(129, 3), 385, 3]-NRT-code), using
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(12841, 3145856, F128, 4, 8) (dual of [(3145856, 4), 12583383, 9]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12845, 3145856, F128, 4, 9) (dual of [(3145856, 4), 12583379, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(12878, 5243006, F128, 4, 12) (dual of [(5243006, 4), 20971946, 13]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 4 | Digital (8, 12, 1048706)-net over F128 | [i] | Net Defined by OOA | |