Information on Result #684830
Linear OA(792, 16838, F7, 20) (dual of [16838, 16746, 21]-code), using construction X applied to Ce(19) ⊂ Ce(14) based on
- linear OA(786, 16807, F7, 20) (dual of [16807, 16721, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(76, 31, F7, 4) (dual of [31, 25, 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 OA(793, 16839, F7, 20) (dual of [16839, 16746, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(794, 16840, F7, 20) (dual of [16840, 16746, 21]-code) | [i] | ||
| 3 | Linear OA(795, 16841, F7, 20) (dual of [16841, 16746, 21]-code) | [i] | ||
| 4 | Linear OA(796, 16842, F7, 20) (dual of [16842, 16746, 21]-code) | [i] | ||
| 5 | Linear OOA(792, 16838, F7, 2, 20) (dual of [(16838, 2), 33584, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(792, 16838, F7, 3, 20) (dual of [(16838, 3), 50422, 21]-NRT-code) | [i] | ||
| 7 | Digital (72, 92, 16838)-net over F7 | [i] | ||
| 8 | Linear OOA(792, 8419, F7, 2, 20) (dual of [(8419, 2), 16746, 21]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(792, 5612, F7, 3, 20) (dual of [(5612, 3), 16744, 21]-NRT-code) | [i] | ||