Information on Result #1187658
Digital (143, 172, 4682)-net over F4, using net defined by OOA based on linear OOA(4172, 4682, F4, 29, 29) (dual of [(4682, 29), 135606, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4172, 65549, F4, 29) (dual of [65549, 65377, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4172, 65555, F4, 29) (dual of [65555, 65383, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(43, 19, F4, 2) (dual of [19, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- construction X applied to Ce(28) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(4172, 65555, F4, 29) (dual of [65555, 65383, 30]-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 (144, 172, 4682)-net over F4 | [i] | t-Expansion | |
| 2 | Digital (144, 173, 4682)-net over F4 | [i] | Net Duplication | |
| 3 | Digital (143, 171, 4682)-net over F4 | [i] | m-Reduction | |