Information on Result #684453
Linear OA(750, 5764810, F7, 8) (dual of [5764810, 5764760, 9]-code), using construction X applied to Ce(7) ⊂ Ce(5) based on
- linear OA(749, 5764801, F7, 8) (dual of [5764801, 5764752, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(741, 5764801, F7, 6) (dual of [5764801, 5764760, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(71, 9, F7, 1) (dual of [9, 8, 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(750, 3978364, F7, 2, 8) (dual of [(3978364, 2), 7956678, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(750, 3978364, F7, 3, 8) (dual of [(3978364, 3), 11935042, 9]-NRT-code) | [i] | ||
| 3 | Digital (42, 50, 3978364)-net over F7 | [i] | ||
| 4 | Linear OOA(750, 2882405, F7, 2, 8) (dual of [(2882405, 2), 5764760, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(750, 1921603, F7, 3, 8) (dual of [(1921603, 3), 5764759, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(750, 1441202, F7, 8, 8) (dual of [(1441202, 8), 11529566, 9]-NRT-code) | [i] | OA Folding and Stacking | |