Information on Result #699116
Linear OA(8126, 531449, F81, 9) (dual of [531449, 531423, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,3]) based on
- linear OA(8125, 531442, F81, 9) (dual of [531442, 531417, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(8119, 531442, F81, 7) (dual of [531442, 531423, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(811, 7, F81, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(952, 1062898, F9, 9) (dual of [1062898, 1062846, 10]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8126, 276594, F81, 2, 9) (dual of [(276594, 2), 553162, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8126, 276594, F81, 3, 9) (dual of [(276594, 3), 829756, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(8126, 276594, F81, 4, 9) (dual of [(276594, 4), 1106350, 10]-NRT-code) | [i] | ||
| 5 | Digital (17, 26, 276594)-net over F81 | [i] | ||
| 6 | Linear OOA(8126, 265724, F81, 2, 9) (dual of [(265724, 2), 531422, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8126, 177149, F81, 3, 9) (dual of [(177149, 3), 531421, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(8126, 132862, F81, 4, 9) (dual of [(132862, 4), 531422, 10]-NRT-code) | [i] | ||
| 9 | Linear OOA(8126, 132862, F81, 9, 9) (dual of [(132862, 9), 1195732, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |