Information on Result #699998
Linear OA(12862, 16395, F128, 30) (dual of [16395, 16333, 31]-code), using construction X applied to Ce(29) ⊂ Ce(25) based on
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(12851, 16384, F128, 26) (dual of [16384, 16333, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), 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(16109, 16395, S16, 30) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3287, 16395, S32, 30) | [i] | ||
| 3 | OA(6473, 16395, S64, 30) | [i] | ||
| 4 | Linear OOA(12862, 8197, F128, 2, 30) (dual of [(8197, 2), 16332, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12862, 5465, F128, 3, 30) (dual of [(5465, 3), 16333, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(12862, 1093, F128, 30, 30) (dual of [(1093, 30), 32728, 31]-NRT-code) | [i] | OA Folding and Stacking | |