Information on Result #684466
Linear OA(782, 5764818, F7, 12) (dual of [5764818, 5764736, 13]-code), using construction X applied to Ce(11) ⊂ Ce(9) based on
- linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 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(71, 17, F7, 1) (dual of [17, 16, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 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(782, 5285897, F7, 2, 12) (dual of [(5285897, 2), 10571712, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(782, 5285897, F7, 3, 12) (dual of [(5285897, 3), 15857609, 13]-NRT-code) | [i] | ||
| 3 | Digital (70, 82, 5285897)-net over F7 | [i] | ||
| 4 | Linear OOA(782, 2882409, F7, 2, 12) (dual of [(2882409, 2), 5764736, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(782, 1921606, F7, 3, 12) (dual of [(1921606, 3), 5764736, 13]-NRT-code) | [i] | ||
| 6 | Linear OOA(782, 960803, F7, 12, 12) (dual of [(960803, 12), 11529554, 13]-NRT-code) | [i] | OA Folding and Stacking | |