Information on Result #699880
Linear OA(12854, 16414, F128, 23) (dual of [16414, 16360, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,6]) based on
- linear OA(12845, 16385, F128, 23) (dual of [16385, 16340, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12825, 16385, F128, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(6463, 16414, S64, 23) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12854, 14210, F128, 2, 23) (dual of [(14210, 2), 28366, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12854, 14210, F128, 3, 23) (dual of [(14210, 3), 42576, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(12854, 14210, F128, 4, 23) (dual of [(14210, 4), 56786, 24]-NRT-code) | [i] | ||
| 5 | Digital (31, 54, 14210)-net over F128 | [i] | ||
| 6 | Linear OOA(12854, 8207, F128, 2, 23) (dual of [(8207, 2), 16360, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12854, 5471, F128, 3, 23) (dual of [(5471, 3), 16359, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(12854, 4103, F128, 4, 23) (dual of [(4103, 4), 16358, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(12854, 1492, F128, 23, 23) (dual of [(1492, 23), 34262, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |