Information on Result #699675
Linear OA(12878, 2097176, F128, 25) (dual of [2097176, 2097098, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) 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(12855, 2097153, F128, 19) (dual of [2097153, 2097098, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), 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(32110, 2097176, S32, 25) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6491, 2097176, S64, 25) | [i] | ||
| 3 | Linear OOA(12878, 1048588, F128, 2, 25) (dual of [(1048588, 2), 2097098, 26]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(12878, 699058, F128, 3, 25) (dual of [(699058, 3), 2097096, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(12878, 524294, F128, 4, 25) (dual of [(524294, 4), 2097098, 26]-NRT-code) | [i] | ||