Information on Result #699144
Linear OA(8182, 531481, F81, 25) (dual of [531481, 531399, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,7]) based on
- linear OA(8173, 531442, F81, 25) (dual of [531442, 531369, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(8143, 531442, F81, 15) (dual of [531442, 531399, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(819, 39, F81, 9) (dual of [39, 30, 10]-code or 39-arc in PG(8,81)), using
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), using
- Reed–Solomon code RS(72,81) [i]
- discarding factors / shortening the dual code based on linear OA(819, 81, F81, 9) (dual of [81, 72, 10]-code or 81-arc in PG(8,81)), 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(8182, 531481, F81, 2, 25) (dual of [(531481, 2), 1062880, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8182, 531481, F81, 3, 25) (dual of [(531481, 3), 1594361, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(8182, 531481, F81, 4, 25) (dual of [(531481, 4), 2125842, 26]-NRT-code) | [i] | ||
| 4 | Digital (57, 82, 531481)-net over F81 | [i] | ||
| 5 | Linear OOA(8182, 265740, F81, 2, 25) (dual of [(265740, 2), 531398, 26]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8182, 177160, F81, 3, 25) (dual of [(177160, 3), 531398, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(8182, 132870, F81, 4, 25) (dual of [(132870, 4), 531398, 26]-NRT-code) | [i] | ||
| 8 | Linear OOA(8182, 44290, F81, 25, 25) (dual of [(44290, 25), 1107168, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |