Information on Result #699850
Linear OA(12820, 16396, F128, 9) (dual of [16396, 16376, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- 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(1289, 16385, F128, 5) (dual of [16385, 16376, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1283, 11, F128, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), 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(6424, 16396, S64, 9) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12820, 13951, F128, 2, 9) (dual of [(13951, 2), 27882, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12820, 13951, F128, 3, 9) (dual of [(13951, 3), 41833, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(12820, 13951, F128, 4, 9) (dual of [(13951, 4), 55784, 10]-NRT-code) | [i] | ||
| 5 | Digital (11, 20, 13951)-net over F128 | [i] | ||
| 6 | Linear OOA(12820, 8198, F128, 2, 9) (dual of [(8198, 2), 16376, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12820, 5465, F128, 3, 9) (dual of [(5465, 3), 16375, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(12820, 4099, F128, 4, 9) (dual of [(4099, 4), 16376, 10]-NRT-code) | [i] | ||
| 9 | Linear OOA(12820, 4098, F128, 9, 9) (dual of [(4098, 9), 36862, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |