Information on Result #2279158
Linear OA(783, 16820, F7, 19) (dual of [16820, 16737, 20]-code), using 1 times code embedding in larger space based on linear OA(782, 16819, F7, 19) (dual of [16819, 16737, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- 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(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(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 OOA(783, 14251, F7, 2, 19) (dual of [(14251, 2), 28419, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(783, 14251, F7, 3, 19) (dual of [(14251, 3), 42670, 20]-NRT-code) | [i] | ||
| 3 | Digital (64, 83, 14251)-net over F7 | [i] | ||
| 4 | Linear OOA(783, 8410, F7, 2, 19) (dual of [(8410, 2), 16737, 20]-NRT-code) | [i] | OOA Folding | |