Information on Result #699876
Linear OA(12870, 16414, F128, 31) (dual of [16414, 16344, 32]-code), using construction X applied to C([0,15]) ⊂ C([0,10]) based on
- linear OA(12861, 16385, F128, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(12841, 16385, F128, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [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(6482, 16414, S64, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12870, 9471, F128, 2, 31) (dual of [(9471, 2), 18872, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12870, 9471, F128, 3, 31) (dual of [(9471, 3), 28343, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(12870, 9471, F128, 4, 31) (dual of [(9471, 4), 37814, 32]-NRT-code) | [i] | ||
| 5 | Digital (39, 70, 9471)-net over F128 | [i] | ||
| 6 | Linear OOA(12870, 8207, F128, 2, 31) (dual of [(8207, 2), 16344, 32]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12870, 5471, F128, 3, 31) (dual of [(5471, 3), 16343, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(12870, 4103, F128, 4, 31) (dual of [(4103, 4), 16342, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(12870, 1094, F128, 31, 31) (dual of [(1094, 31), 33844, 32]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |