Information on Result #700105
Linear OA(12868, 16413, F128, 30) (dual of [16413, 16345, 31]-code), using construction X applied to Ce(29) ⊂ Ce(19) 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(12839, 16384, F128, 20) (dual of [16384, 16345, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1289, 29, F128, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
- Reed–Solomon code RS(119,128) [i]
- discarding factors / shortening the dual code based on linear OA(1289, 128, F128, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), 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(6480, 16413, S64, 30) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12868, 9792, F128, 2, 30) (dual of [(9792, 2), 19516, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12868, 9792, F128, 3, 30) (dual of [(9792, 3), 29308, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(12868, 9792, F128, 4, 30) (dual of [(9792, 4), 39100, 31]-NRT-code) | [i] | ||
| 5 | Digital (38, 68, 9792)-net over F128 | [i] | ||
| 6 | Linear OOA(12868, 8206, F128, 2, 30) (dual of [(8206, 2), 16344, 31]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12868, 5471, F128, 3, 30) (dual of [(5471, 3), 16345, 31]-NRT-code) | [i] | ||
| 8 | Linear OOA(12868, 4103, F128, 4, 30) (dual of [(4103, 4), 16344, 31]-NRT-code) | [i] | ||