Information on Result #953172
Linear OOA(3180, 177166, F3, 3, 22) (dual of [(177166, 3), 531318, 23]-NRT-code), using OOA 3-folding based on linear OA(3180, 531498, F3, 22) (dual of [531498, 531318, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3180, 531500, F3, 22) (dual of [531500, 531320, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3121, 531441, F3, 16) (dual of [531441, 531320, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(311, 59, F3, 5) (dual of [59, 48, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(3180, 177166, F3, 4, 22) (dual of [(177166, 4), 708484, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3180, 177166, F3, 5, 22) (dual of [(177166, 5), 885650, 23]-NRT-code) | [i] | ||
| 3 | Digital (158, 180, 177166)-net over F3 | [i] | ||