Information on Result #1202652
Digital (56, 73, 1048615)-net over F81, using net defined by OOA based on linear OOA(8173, 1048615, F81, 20, 17) (dual of [(1048615, 20), 20972227, 18]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8173, 2097231, F81, 4, 17) (dual of [(2097231, 4), 8388851, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8173, 2097232, F81, 4, 17) (dual of [(2097232, 4), 8388855, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(818, 82, F81, 4, 8) (dual of [(82, 4), 320, 9]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;320,81) [i]
- linear OOA(8165, 2097150, F81, 4, 17) (dual of [(2097150, 4), 8388535, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-code), using
- linear OOA(818, 82, F81, 4, 8) (dual of [(82, 4), 320, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8173, 2097232, F81, 4, 17) (dual of [(2097232, 4), 8388855, 18]-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 (129, 146, 2097230)-net over F9 | [i] | Trace Code for Nets | |