Information on Result #1187558
Digital (184, 211, 80664)-net over F4, using net defined by OOA based on linear OOA(4211, 80664, F4, 27, 27) (dual of [(80664, 27), 2177717, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(4211, 1048633, F4, 27) (dual of [1048633, 1048422, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(4201, 1048576, F4, 27) (dual of [1048576, 1048375, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- 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(410, 60, F4, 5) (dual of [60, 50, 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(26) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4211, 1048636, F4, 27) (dual of [1048636, 1048425, 28]-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 (185, 212, 80664)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (186, 213, 80664)-net over F4 | [i] | ||