Information on Result #699653
Linear OA(12868, 2097160, F128, 23) (dual of [2097160, 2097092, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,10]) based on
- linear OA(12867, 2097153, F128, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(16119, 2097160, S16, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3296, 2097160, S32, 23) | [i] | ||
| 3 | OA(6480, 2097160, S64, 23) | [i] | ||
| 4 | Linear OOA(12868, 1048580, F128, 2, 23) (dual of [(1048580, 2), 2097092, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12868, 699053, F128, 3, 23) (dual of [(699053, 3), 2097091, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(12868, 524290, F128, 4, 23) (dual of [(524290, 4), 2097092, 24]-NRT-code) | [i] | ||