Information on Result #731380
Linear OA(970, 1062896, F9, 12) (dual of [1062896, 1062826, 13]-code), using trace code based on linear OA(8135, 531448, F81, 12) (dual of [531448, 531413, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(8134, 531441, F81, 12) (dual of [531441, 531407, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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 OOA(970, 1062896, F9, 2, 12) (dual of [(1062896, 2), 2125722, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(970, 1062896, F9, 3, 12) (dual of [(1062896, 3), 3188618, 13]-NRT-code) | [i] | ||
| 3 | Digital (58, 70, 1062896)-net over F9 | [i] | ||
| 4 | Linear OOA(970, 531448, F9, 2, 12) (dual of [(531448, 2), 1062826, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(970, 354298, F9, 3, 12) (dual of [(354298, 3), 1062824, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(970, 177149, F9, 12, 12) (dual of [(177149, 12), 2125718, 13]-NRT-code) | [i] | OA Folding and Stacking | |