Information on Result #731874
Linear OA(764, 823593, F7, 10) (dual of [823593, 823529, 11]-code), using (u, u+v)-construction based on
- linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- linear OA(757, 823550, F7, 10) (dual of [823550, 823493, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(750, 823543, F7, 9) (dual of [823543, 823493, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
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(764, 823593, F7, 2, 10) (dual of [(823593, 2), 1647122, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(764, 823593, F7, 3, 10) (dual of [(823593, 3), 2470715, 11]-NRT-code) | [i] | ||
| 3 | Digital (54, 64, 823593)-net over F7 | [i] | ||
| 4 | Linear OOA(764, 411796, F7, 2, 10) (dual of [(411796, 2), 823528, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(764, 274531, F7, 3, 10) (dual of [(274531, 3), 823529, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(764, 164718, F7, 10, 10) (dual of [(164718, 10), 1647116, 11]-NRT-code) | [i] | OA Folding and Stacking | |