Information on Result #684532
Linear OA(736, 823550, F7, 6) (dual of [823550, 823514, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(736, 823543, F7, 6) (dual of [823543, 823507, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(729, 823543, F7, 5) (dual of [823543, 823514, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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
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 OA(740, 823600, F7, 6) (dual of [823600, 823560, 7]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(736, 823550, F7, 2, 6) (dual of [(823550, 2), 1647064, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(736, 823550, F7, 3, 6) (dual of [(823550, 3), 2470614, 7]-NRT-code) | [i] | ||
| 4 | Digital (30, 36, 823550)-net over F7 | [i] | ||
| 5 | Linear OOA(736, 411775, F7, 2, 6) (dual of [(411775, 2), 823514, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(736, 274516, F7, 3, 6) (dual of [(274516, 3), 823512, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(736, 274516, F7, 6, 6) (dual of [(274516, 6), 1647060, 7]-NRT-code) | [i] | OA Folding and Stacking | |