Information on Result #1202098
Digital (34, 42, 4194300)-net over F81, using net defined by OOA based on linear OOA(8142, 4194300, F81, 10, 8) (dual of [(4194300, 10), 41942958, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(8142, 8388601, F81, 2, 8) (dual of [(8388601, 2), 16777160, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8142, 8388602, F81, 2, 8) (dual of [(8388602, 2), 16777162, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8113, 4194301, F81, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8113, 8388602, F81, 4) (dual of [8388602, 8388589, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(8113, large, F81, 4) (dual of [large, large−13, 5]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(8113, large, F81, 4) (dual of [large, large−13, 5]-code), using
- OOA 2-folding [i] based on linear OA(8113, 8388602, F81, 4) (dual of [8388602, 8388589, 5]-code), using
- linear OOA(8129, 4194301, F81, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F81, 8) (dual of [large, large−29, 9]-code), using
- OOA 2-folding [i] based on linear OA(8129, 8388602, F81, 8) (dual of [8388602, 8388573, 9]-code), using
- linear OOA(8113, 4194301, F81, 2, 4) (dual of [(4194301, 2), 8388589, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(8142, 8388602, F81, 2, 8) (dual of [(8388602, 2), 16777162, 9]-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 (35, 43, 4194300)-net over F81 | [i] | Net Duplication | |
| 2 | Digital (76, 84, 8388600)-net over F9 | [i] | Trace Code for Nets | |