Information on Result #1187904
Digital (217, 251, 61681)-net over F4, using net defined by OOA based on linear OOA(4251, 61681, F4, 34, 34) (dual of [(61681, 34), 2096903, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(4251, 1048577, F4, 34) (dual of [1048577, 1048326, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4251, 1048586, F4, 34) (dual of [1048586, 1048335, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- linear OA(4251, 1048576, F4, 34) (dual of [1048576, 1048325, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4241, 1048576, F4, 33) (dual of [1048576, 1048335, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(40, 10, F4, 0) (dual of [10, 10, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(33) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(4251, 1048586, F4, 34) (dual of [1048586, 1048335, 35]-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 (218, 252, 61681)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (219, 253, 61681)-net over F4 | [i] | ||