Information on Result #684713
Linear OA(772, 16819, F7, 17) (dual of [16819, 16747, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(771, 16808, F7, 17) (dual of [16808, 16737, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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(773, 16820, F7, 17) (dual of [16820, 16747, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(774, 16821, F7, 17) (dual of [16821, 16747, 18]-code) | [i] | ||
| 3 | Linear OOA(772, 10700, F7, 2, 17) (dual of [(10700, 2), 21328, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(772, 10700, F7, 3, 17) (dual of [(10700, 3), 32028, 18]-NRT-code) | [i] | ||
| 5 | Digital (55, 72, 10700)-net over F7 | [i] | ||
| 6 | Linear OA(774, 16822, F7, 17) (dual of [16822, 16748, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(772, 8409, F7, 2, 17) (dual of [(8409, 2), 16746, 18]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(772, 5606, F7, 3, 17) (dual of [(5606, 3), 16746, 18]-NRT-code) | [i] | ||
| 9 | Linear OOA(772, 2102, F7, 17, 17) (dual of [(2102, 17), 35662, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |