Information on Result #1201002
Digital (31, 39, 2162686)-net over F64, using net defined by OOA based on linear OOA(6439, 2162686, F64, 10, 8) (dual of [(2162686, 10), 21626821, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(6439, 4325373, F64, 2, 8) (dual of [(4325373, 2), 8650707, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(6439, 4325374, F64, 2, 8) (dual of [(4325374, 2), 8650709, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(6410, 131073, F64, 2, 4) (dual of [(131073, 2), 262136, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- OOA 2-folding [i] based on linear OA(6410, 262146, F64, 4) (dual of [262146, 262136, 5]-code), using
- linear OOA(6429, 4194301, F64, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(6429, large, F64, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(6429, 8388602, F64, 8) (dual of [8388602, 8388573, 9]-code), using
- linear OOA(6410, 131073, F64, 2, 4) (dual of [(131073, 2), 262136, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(6439, 4325374, F64, 2, 8) (dual of [(4325374, 2), 8650709, 9]-NRT-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 (70, 78, 4325372)-net over F8 | [i] | Trace Code for Nets | |