Information on Result #700098
Linear OA(12851, 16410, F128, 22) (dual of [16410, 16359, 23]-code), using construction X applied to Ce(21) ⊂ Ce(12) based on
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(12825, 16384, F128, 13) (dual of [16384, 16359, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(1288, 26, F128, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,128)), using
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), using
- Reed–Solomon code RS(120,128) [i]
- discarding factors / shortening the dual code based on linear OA(1288, 128, F128, 8) (dual of [128, 120, 9]-code or 128-arc in PG(7,128)), 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(6460, 16410, S64, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12851, 12112, F128, 2, 22) (dual of [(12112, 2), 24173, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12851, 12112, F128, 3, 22) (dual of [(12112, 3), 36285, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(12851, 12112, F128, 4, 22) (dual of [(12112, 4), 48397, 23]-NRT-code) | [i] | ||
| 5 | Digital (29, 51, 12112)-net over F128 | [i] | ||
| 6 | Linear OOA(12851, 8205, F128, 2, 22) (dual of [(8205, 2), 16359, 23]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12851, 5470, F128, 3, 22) (dual of [(5470, 3), 16359, 23]-NRT-code) | [i] | ||
| 8 | Linear OOA(12851, 4102, F128, 4, 22) (dual of [(4102, 4), 16357, 23]-NRT-code) | [i] | ||