Information on Result #699652
Linear OA(12874, 2097160, F128, 25) (dual of [2097160, 2097086, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,11]) based on
- linear OA(12873, 2097153, F128, 25) (dual of [2097153, 2097080, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 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(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(16130, 2097160, S16, 25) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(32104, 2097160, S32, 25) | [i] | ||
| 3 | OA(6487, 2097160, S64, 25) | [i] | ||
| 4 | Linear OOA(12874, 1048580, F128, 2, 25) (dual of [(1048580, 2), 2097086, 26]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12874, 699053, F128, 3, 25) (dual of [(699053, 3), 2097085, 26]-NRT-code) | [i] | ||
| 6 | Linear OOA(12874, 524290, F128, 4, 25) (dual of [(524290, 4), 2097086, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(12874, 174763, F128, 25, 25) (dual of [(174763, 25), 4369001, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |