Information on Result #699885
Linear OA(12864, 16420, F128, 27) (dual of [16420, 16356, 28]-code), using construction X applied to C([0,13]) ⊂ C([0,7]) based on
- linear OA(12853, 16385, F128, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(12829, 16385, F128, 15) (dual of [16385, 16356, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12811, 35, F128, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), using
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- Reed–Solomon code RS(117,128) [i]
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), 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(6475, 16420, S64, 27) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12864, 16356, F128, 2, 27) (dual of [(16356, 2), 32648, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12864, 16356, F128, 3, 27) (dual of [(16356, 3), 49004, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(12864, 16356, F128, 4, 27) (dual of [(16356, 4), 65360, 28]-NRT-code) | [i] | ||
| 5 | Digital (37, 64, 16356)-net over F128 | [i] | ||
| 6 | Linear OOA(12864, 8210, F128, 2, 27) (dual of [(8210, 2), 16356, 28]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12864, 5473, F128, 3, 27) (dual of [(5473, 3), 16355, 28]-NRT-code) | [i] | ||
| 8 | Linear OOA(12864, 4105, F128, 4, 27) (dual of [(4105, 4), 16356, 28]-NRT-code) | [i] | ||
| 9 | Linear OOA(12864, 1263, F128, 27, 27) (dual of [(1263, 27), 34037, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |