Information on Result #684832
Linear OA(783, 16839, F7, 18) (dual of [16839, 16756, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
- linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-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 OA(784, 16840, F7, 18) (dual of [16840, 16756, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(785, 16841, F7, 18) (dual of [16841, 16756, 19]-code) | [i] | ||
| 3 | Linear OA(786, 16842, F7, 18) (dual of [16842, 16756, 19]-code) | [i] | ||
| 4 | Linear OOA(783, 16839, F7, 2, 18) (dual of [(16839, 2), 33595, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(783, 16839, F7, 3, 18) (dual of [(16839, 3), 50434, 19]-NRT-code) | [i] | ||
| 6 | Digital (65, 83, 16839)-net over F7 | [i] | ||
| 7 | Linear OOA(783, 8419, F7, 2, 18) (dual of [(8419, 2), 16755, 19]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(783, 5613, F7, 3, 18) (dual of [(5613, 3), 16756, 19]-NRT-code) | [i] | ||
| 9 | Linear OOA(783, 1871, F7, 18, 18) (dual of [(1871, 18), 33595, 19]-NRT-code) | [i] | OA Folding and Stacking | |