Information on Result #1205093
Digital (162, 176, 1366568)-net over F3, using trace code for nets based on digital (74, 88, 683284)-net over F9, using
- net defined by OOA [i] based on linear OOA(988, 683284, F9, 14, 14) (dual of [(683284, 14), 9565888, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(988, 4782988, F9, 14) (dual of [4782988, 4782900, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(988, 4782993, F9, 14) (dual of [4782993, 4782905, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(964, 4782969, F9, 11) (dual of [4782969, 4782905, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(93, 24, F9, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(988, 4782993, F9, 14) (dual of [4782993, 4782905, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(988, 4782988, F9, 14) (dual of [4782988, 4782900, 15]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (163, 177, 1366568)-net over F3 | [i] | Net Duplication | |