Information on Result #952834
Linear OOA(3125, 19691, F3, 3, 19) (dual of [(19691, 3), 58948, 20]-NRT-code), using OOA 3-folding based on linear OA(3125, 59073, F3, 19) (dual of [59073, 58948, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(15) [i] based on
- linear OA(3121, 59049, F3, 19) (dual of [59049, 58928, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(3125, 19691, F3, 3, 18) (dual of [(19691, 3), 58948, 19]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(3126, 19691, F3, 3, 19) (dual of [(19691, 3), 58947, 20]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3125, 19691, F3, 4, 19) (dual of [(19691, 4), 78639, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3125, 19691, F3, 5, 19) (dual of [(19691, 5), 98330, 20]-NRT-code) | [i] | ||
| 5 | Digital (106, 125, 19691)-net over F3 | [i] | ||