Information on Result #1196002
Digital (46, 54, 4194301)-net over F25, using net defined by OOA based on linear OOA(2554, 4194301, F25, 10, 8) (dual of [(4194301, 10), 41942956, 9]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2554, large, F25, 2, 8), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2552, 8388602, F25, 2, 8) (dual of [(8388602, 2), 16777152, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(2516, large, F25, 4) (dual of [large, large−16, 5]-code), using
- OOA 2-folding [i] based on linear OA(2516, 8388602, F25, 4) (dual of [8388602, 8388586, 5]-code), using
- linear OOA(2536, 4194301, F25, 2, 8) (dual of [(4194301, 2), 8388566, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(2536, large, F25, 8) (dual of [large, large−36, 9]-code), using
- OOA 2-folding [i] based on linear OA(2536, 8388602, F25, 8) (dual of [8388602, 8388566, 9]-code), using
- linear OOA(2516, 4194301, F25, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2552, 8388602, F25, 2, 8) (dual of [(8388602, 2), 16777152, 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 (100, 108, 8388602)-net over F5 | [i] | Trace Code for Nets | |
| 2 | Digital (62, 70, 8388602)-net over F25 | [i] | (u, u+v)-Construction for Nets | |