Information on Result #699660
Linear OA(12826, 2097160, F128, 9) (dual of [2097160, 2097134, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- linear OA(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(12819, 2097153, F128, 7) (dual of [2097153, 2097134, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 | OA(1646, 2097160, S16, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3237, 2097160, S32, 9) | [i] | ||
| 3 | OA(6431, 2097160, S64, 9) | [i] | ||
| 4 | Linear OOA(12826, 1048580, F128, 2, 9) (dual of [(1048580, 2), 2097134, 10]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12826, 699053, F128, 3, 9) (dual of [(699053, 3), 2097133, 10]-NRT-code) | [i] | ||
| 6 | Linear OOA(12826, 524290, F128, 4, 9) (dual of [(524290, 4), 2097134, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(12826, 524289, F128, 9, 9) (dual of [(524289, 9), 4718575, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |