Information on Result #699741
Linear OA(12869, 2097163, F128, 23) (dual of [2097163, 2097094, 24]-code), using construction X applied to Ce(22) ⊂ Ce(19) based on
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), 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(16121, 2097163, S16, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3297, 2097163, S32, 23) | [i] | ||
| 3 | OA(6481, 2097163, S64, 23) | [i] | ||
| 4 | Linear OOA(12869, 1048581, F128, 2, 23) (dual of [(1048581, 2), 2097093, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(12869, 699054, F128, 3, 23) (dual of [(699054, 3), 2097093, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(12869, 190651, F128, 23, 23) (dual of [(190651, 23), 4384904, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |