Information on Result #699136
Linear OA(8154, 531465, F81, 17) (dual of [531465, 531411, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(815, 23, F81, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,81)), using
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), using
- Reed–Solomon code RS(76,81) [i]
- discarding factors / shortening the dual code based on linear OA(815, 81, F81, 5) (dual of [81, 76, 6]-code or 81-arc in PG(4,81)), 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(8154, 444615, F81, 2, 17) (dual of [(444615, 2), 889176, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8154, 444615, F81, 3, 17) (dual of [(444615, 3), 1333791, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(8154, 444615, F81, 4, 17) (dual of [(444615, 4), 1778406, 18]-NRT-code) | [i] | ||
| 4 | Digital (37, 54, 444615)-net over F81 | [i] | ||
| 5 | Linear OOA(8154, 265732, F81, 2, 17) (dual of [(265732, 2), 531410, 18]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8154, 177155, F81, 3, 17) (dual of [(177155, 3), 531411, 18]-NRT-code) | [i] | ||
| 7 | Linear OOA(8154, 132866, F81, 4, 17) (dual of [(132866, 4), 531410, 18]-NRT-code) | [i] | ||
| 8 | Linear OOA(8154, 66433, F81, 17, 17) (dual of [(66433, 17), 1129307, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |