Information on Result #2677277
Linear OOA(3160, 177152, F3, 3, 20) (dual of [(177152, 3), 531296, 21]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(3157, 177151, F3, 3, 20) (dual of [(177151, 3), 531296, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3157, 531453, F3, 20) (dual of [531453, 531296, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3157, 531441, F3, 20) (dual of [531441, 531284, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [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(3160, 163388, F3, 4, 20) (dual of [(163388, 4), 653392, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3160, 163388, F3, 5, 20) (dual of [(163388, 5), 816780, 21]-NRT-code) | [i] | ||
| 3 | Digital (140, 160, 163388)-net over F3 | [i] | ||