Information on Result #1204514
Digital (42, 54, 2796456)-net over F256, using net defined by OOA based on linear OOA(25654, 2796456, F256, 18, 12) (dual of [(2796456, 18), 50336154, 13]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25654, 2796457, F256, 6, 12) (dual of [(2796457, 6), 16778688, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(2564, 257, F256, 6, 4) (dual of [(257, 6), 1538, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;1538,256) [i]
- linear OOA(25616, 1398100, F256, 6, 6) (dual of [(1398100, 6), 8388584, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- discarding factors / shortening the dual code based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- linear OOA(25634, 1398100, F256, 6, 12) (dual of [(1398100, 6), 8388566, 13]-NRT-code), using
- OOA 6-folding [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- OOA 6-folding [i] based on linear OA(25634, 8388600, F256, 12) (dual of [8388600, 8388566, 13]-code), using
- linear OOA(2564, 257, F256, 6, 4) (dual of [(257, 6), 1538, 5]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
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 (96, 108, 5592912)-net over F16 | [i] | Trace Code for Nets | |