Information on Result #684711
Linear OA(792, 16819, F7, 21) (dual of [16819, 16727, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(791, 16808, F7, 21) (dual of [16808, 16717, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(781, 16808, F7, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 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 OA(793, 16820, F7, 21) (dual of [16820, 16727, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(792, 14733, F7, 2, 21) (dual of [(14733, 2), 29374, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(792, 14733, F7, 3, 21) (dual of [(14733, 3), 44107, 22]-NRT-code) | [i] | ||
| 4 | Digital (71, 92, 14733)-net over F7 | [i] | ||
| 5 | Linear OOA(792, 8409, F7, 2, 21) (dual of [(8409, 2), 16726, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(792, 5606, F7, 3, 21) (dual of [(5606, 3), 16726, 22]-NRT-code) | [i] | ||