Information on Result #699146
Linear OA(8170, 531481, F81, 21) (dual of [531481, 531411, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,5]) based on
- linear OA(8161, 531442, F81, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(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(8170, 531481, F81, 2, 21) (dual of [(531481, 2), 1062892, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8170, 531481, F81, 3, 21) (dual of [(531481, 3), 1594373, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8170, 531481, F81, 4, 21) (dual of [(531481, 4), 2125854, 22]-NRT-code) | [i] | ||
| 4 | Digital (49, 70, 531481)-net over F81 | [i] | ||
| 5 | Linear OOA(8170, 265740, F81, 2, 21) (dual of [(265740, 2), 531410, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8170, 177160, F81, 3, 21) (dual of [(177160, 3), 531410, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(8170, 132870, F81, 4, 21) (dual of [(132870, 4), 531410, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(8170, 53148, F81, 21, 21) (dual of [(53148, 21), 1116038, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |