Information on Result #1195410
Digital (50, 69, 7282)-net over F16, using net defined by OOA based on linear OOA(1669, 7282, F16, 19, 19) (dual of [(7282, 19), 138289, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(1669, 65539, F16, 19) (dual of [65539, 65470, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1669, 65540, F16, 19) (dual of [65540, 65471, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1665, 65536, F16, 18) (dual of [65536, 65471, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(160, 4, F16, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(1669, 65540, F16, 19) (dual of [65540, 65471, 20]-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 (51, 70, 7282)-net over F16 | [i] | Net Duplication | |
| 2 | Digital (52, 71, 7282)-net over F16 | [i] | ||
| 3 | (73, 92, 7282)-net in base 8 | [i] | Base Change | |