Information on Result #944863
Linear OOA(12810, 1048577, F128, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code), using OA 2-folding and stacking 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
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(12812, 1048706, F128, 3, 4) (dual of [(1048706, 3), 3146106, 5]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(12839, 3844778, F128, 3, 8) (dual of [(3844778, 3), 11534295, 9]-NRT-code) | [i] | ||
| 3 | Linear OOA(12843, 3844778, F128, 3, 9) (dual of [(3844778, 3), 11534291, 10]-NRT-code) | [i] | ||
| 4 | OOA(12839, 3844778, S128, 3, 9) | [i] | ||
| 5 | Linear OOA(12849, 7591758, F128, 3, 9) (dual of [(7591758, 3), 22775225, 10]-NRT-code) | [i] | Generalized (u, u+v)-Construction for OOAs | |
| 6 | Linear OOA(12850, large, F128, 3, 9) | [i] | ||
| 7 | Linear OOA(12844, large, F128, 3, 8) | [i] | ||
| 8 | Linear OOA(12816, large, F128, 3, 4) | [i] | ||
| 9 | Linear OOA(12878, 6990510, F128, 3, 12) (dual of [(6990510, 3), 20971452, 13]-NRT-code) | [i] | ||
| 10 | Linear OOA(12877, 6291459, F128, 3, 12) (dual of [(6291459, 3), 18874300, 13]-NRT-code) | [i] | ||
| 11 | Linear OOA(12876, 6640979, F128, 3, 12) (dual of [(6640979, 3), 19922861, 13]-NRT-code) | [i] | ||