Information on Result #952646
Linear OOA(3137, 177156, F3, 3, 17) (dual of [(177156, 3), 531331, 18]-NRT-code), using OOA 3-folding based on linear OA(3137, 531468, F3, 17) (dual of [531468, 531331, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3137, 531469, F3, 17) (dual of [531469, 531332, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(34, 28, F3, 2) (dual of [28, 24, 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(16) ⊂ Ce(13) [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(3138, 177156, F3, 3, 17) (dual of [(177156, 3), 531330, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3137, 177156, F3, 4, 17) (dual of [(177156, 4), 708487, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3137, 177156, F3, 5, 17) (dual of [(177156, 5), 885643, 18]-NRT-code) | [i] | ||
| 4 | Digital (120, 137, 177156)-net over F3 | [i] | ||