Information on Result #952647
Linear OOA(3139, 177161, F3, 3, 17) (dual of [(177161, 3), 531344, 18]-NRT-code), using OOA 3-folding based on linear OA(3139, 531483, F3, 17) (dual of [531483, 531344, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [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(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), 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(3142, 177162, F3, 3, 17) (dual of [(177162, 3), 531344, 18]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(3140, 177161, F3, 3, 17) (dual of [(177161, 3), 531343, 18]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(3141, 177161, F3, 3, 17) (dual of [(177161, 3), 531342, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(3139, 177161, F3, 4, 17) (dual of [(177161, 4), 708505, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3139, 177161, F3, 5, 17) (dual of [(177161, 5), 885666, 18]-NRT-code) | [i] | ||
| 6 | Digital (122, 139, 177161)-net over F3 | [i] | ||