Information on Result #1191648
Digital (61, 74, 87382)-net over F8, using net defined by OOA based on linear OOA(874, 87382, F8, 13, 13) (dual of [(87382, 13), 1135892, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(874, 524293, F8, 13) (dual of [524293, 524219, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(874, 524294, F8, 13) (dual of [524294, 524220, 14]-code), using
- trace code [i] based on linear OA(6437, 262147, F64, 13) (dual of [262147, 262110, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(6437, 262144, F64, 13) (dual of [262144, 262107, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(6434, 262144, F64, 12) (dual of [262144, 262110, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(6437, 262147, F64, 13) (dual of [262147, 262110, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(874, 524294, F8, 13) (dual of [524294, 524220, 14]-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 (62, 75, 87382)-net over F8 | [i] | Net Duplication | |