Information on Result #731875
Linear OA(772, 5764852, F7, 10) (dual of [5764852, 5764780, 11]-code), using (u, u+v)-construction based on
- linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- linear OA(765, 5764809, F7, 10) (dual of [5764809, 5764744, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(765, 5764801, F7, 10) (dual of [5764801, 5764736, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 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(772, 5764852, F7, 2, 10) (dual of [(5764852, 2), 11529632, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(772, 5764852, F7, 3, 10) (dual of [(5764852, 3), 17294484, 11]-NRT-code) | [i] | ||
| 3 | Digital (62, 72, 5764852)-net over F7 | [i] | ||
| 4 | Linear OOA(772, 2882426, F7, 2, 10) (dual of [(2882426, 2), 5764780, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(772, 1921617, F7, 3, 10) (dual of [(1921617, 3), 5764779, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(772, 1152970, F7, 10, 10) (dual of [(1152970, 10), 11529628, 11]-NRT-code) | [i] | OA Folding and Stacking | |