Information on Result #813691
Linear OOA(3136, 29537, F3, 2, 20) (dual of [(29537, 2), 58938, 21]-NRT-code), using OOA 2-folding based on linear OA(3136, 59074, F3, 20) (dual of [59074, 58938, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3135, 59073, F3, 20) (dual of [59073, 58938, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3111, 59049, F3, 17) (dual of [59049, 58938, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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
- construction X applied to Ce(19) ⊂ Ce(16) [i] based on
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(3136, 20674, F3, 3, 20) (dual of [(20674, 3), 61886, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3136, 20674, F3, 4, 20) (dual of [(20674, 4), 82560, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(3136, 20674, F3, 5, 20) (dual of [(20674, 5), 103234, 21]-NRT-code) | [i] | ||
| 4 | Digital (116, 136, 20674)-net over F3 | [i] | ||