Information on Result #954899
Linear OOA(3245, 19691, F3, 3, 37) (dual of [(19691, 3), 58828, 38]-NRT-code), using OOA 3-folding based on linear OA(3245, 59073, F3, 37) (dual of [59073, 58828, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(33) [i] based on
- linear OA(3241, 59049, F3, 37) (dual of [59049, 58808, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(3221, 59049, F3, 34) (dual of [59049, 58828, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(34, 24, F3, 2) (dual of [24, 20, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-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 OOA(3245, 19691, F3, 3, 36) (dual of [(19691, 3), 58828, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3246, 19691, F3, 3, 37) (dual of [(19691, 3), 58827, 38]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3244, 19690, F3, 3, 36) (dual of [(19690, 3), 58826, 37]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(3245, 19691, F3, 4, 37) (dual of [(19691, 4), 78519, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3245, 19691, F3, 5, 37) (dual of [(19691, 5), 98210, 38]-NRT-code) | [i] | ||
| 6 | Digital (208, 245, 19691)-net over F3 | [i] | ||