Information on Result #954239
Linear OOA(3205, 19691, F3, 3, 31) (dual of [(19691, 3), 58868, 32]-NRT-code), using OOA 3-folding based on linear OA(3205, 59073, F3, 31) (dual of [59073, 58868, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3181, 59049, F3, 28) (dual of [59049, 58868, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(3205, 19691, F3, 3, 30) (dual of [(19691, 3), 58868, 31]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3206, 19691, F3, 3, 31) (dual of [(19691, 3), 58867, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3204, 19690, F3, 3, 30) (dual of [(19690, 3), 58866, 31]-NRT-code) | [i] | Truncation for OOAs | |
| 4 | Linear OOA(3205, 19691, F3, 4, 31) (dual of [(19691, 4), 78559, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3205, 19691, F3, 5, 31) (dual of [(19691, 5), 98250, 32]-NRT-code) | [i] | ||
| 6 | Digital (174, 205, 19691)-net over F3 | [i] | ||