Information on Result #1187074
Digital (140, 161, 104862)-net over F4, using net defined by OOA based on linear OOA(4161, 104862, F4, 21, 21) (dual of [(104862, 21), 2201941, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4161, 1048621, F4, 21) (dual of [1048621, 1048460, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4161, 1048626, F4, 21) (dual of [1048626, 1048465, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- linear OA(4151, 1048576, F4, 21) (dual of [1048576, 1048425, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4111, 1048576, F4, 15) (dual of [1048576, 1048465, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(410, 50, F4, 5) (dual of [50, 40, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4161, 1048626, F4, 21) (dual of [1048626, 1048465, 22]-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 (140, 160, 104862)-net over F4 | [i] | m-Reduction | |