Information on Result #3186587
Digital (173, 195, 11919)-net over F2, using t-expansion based on digital (172, 195, 11919)-net over F2, using
- net defined by OOA [i] based on linear OOA(2195, 11919, F2, 23, 23) (dual of [(11919, 23), 273942, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2195, 131110, F2, 23) (dual of [131110, 130915, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- linear OA(2188, 131072, F2, 23) (dual of [131072, 130884, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2154, 131072, F2, 19) (dual of [131072, 130918, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2195, 131113, F2, 23) (dual of [131113, 130918, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2195, 131110, F2, 23) (dual of [131110, 130915, 24]-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 (174, 196, 11919)-net over F2 | [i] | Net Duplication | |
| 2 | Digital (175, 197, 11919)-net over F2 | [i] | ||