Information on Result #684577
Linear OA(763, 823577, F7, 10) (dual of [823577, 823514, 11]-code), using construction X applied to Ce(9) ⊂ Ce(4) 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(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(76, 34, F7, 4) (dual of [34, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), using
- 1 times truncation [i] based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(76, 42, F7, 4) (dual of [42, 36, 5]-code), 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(763, 823577, F7, 2, 10) (dual of [(823577, 2), 1647091, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(763, 823577, F7, 3, 10) (dual of [(823577, 3), 2470668, 11]-NRT-code) | [i] | ||
| 3 | Digital (53, 63, 823577)-net over F7 | [i] | ||
| 4 | Linear OOA(763, 411788, F7, 2, 10) (dual of [(411788, 2), 823513, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(763, 274525, F7, 3, 10) (dual of [(274525, 3), 823512, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(763, 164715, F7, 10, 10) (dual of [(164715, 10), 1647087, 11]-NRT-code) | [i] | OA Folding and Stacking | |