Information on Result #699862
Linear OA(12834, 16402, F128, 15) (dual of [16402, 16368, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,4]) based on
- 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(12817, 16385, F128, 9) (dual of [16385, 16368, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1285, 17, F128, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), 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(6440, 16402, S64, 15) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12834, 9964, F128, 2, 15) (dual of [(9964, 2), 19894, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12834, 9964, F128, 3, 15) (dual of [(9964, 3), 29858, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(12834, 9964, F128, 4, 15) (dual of [(9964, 4), 39822, 16]-NRT-code) | [i] | ||
| 5 | Digital (19, 34, 9964)-net over F128 | [i] | ||
| 6 | Linear OOA(12834, 8201, F128, 2, 15) (dual of [(8201, 2), 16368, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12834, 5467, F128, 3, 15) (dual of [(5467, 3), 16367, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(12834, 4100, F128, 4, 15) (dual of [(4100, 4), 16366, 16]-NRT-code) | [i] | ||
| 9 | Linear OOA(12834, 2343, F128, 15, 15) (dual of [(2343, 15), 35111, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |