Information on Result #699142
Linear OA(8162, 531473, F81, 19) (dual of [531473, 531411, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,5]) based on
- linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8131, 531442, F81, 11) (dual of [531442, 531411, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(817, 31, F81, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,81)), using
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), using
- Reed–Solomon code RS(74,81) [i]
- discarding factors / shortening the dual code based on linear OA(817, 81, F81, 7) (dual of [81, 74, 8]-code or 81-arc in PG(6,81)), 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 | Linear OOA(8162, 531473, F81, 2, 19) (dual of [(531473, 2), 1062884, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8162, 531473, F81, 3, 19) (dual of [(531473, 3), 1594357, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(8162, 531473, F81, 4, 19) (dual of [(531473, 4), 2125830, 20]-NRT-code) | [i] | ||
| 4 | Digital (43, 62, 531473)-net over F81 | [i] | ||
| 5 | Linear OOA(8162, 265736, F81, 2, 19) (dual of [(265736, 2), 531410, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8162, 177157, F81, 3, 19) (dual of [(177157, 3), 531409, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(8162, 132868, F81, 4, 19) (dual of [(132868, 4), 531410, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(8162, 59052, F81, 19, 19) (dual of [(59052, 19), 1121926, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |