Information on Result #1204518
Digital (44, 56, 2828839)-net over F256, using net defined by OOA based on linear OOA(25656, 2828839, F256, 18, 12) (dual of [(2828839, 18), 50919046, 13]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25656, 2828840, F256, 6, 12) (dual of [(2828840, 6), 16972984, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(2566, 32640, F256, 6, 4) (dual of [(32640, 6), 195834, 5]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- 1 times truncation [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- OA 2-folding and stacking [i] based on linear OA(2566, 65280, F256, 4) (dual of [65280, 65274, 5]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(2566, 32640, F256, 4, 4) (dual of [(32640, 4), 130554, 5]-NRT-code), using
- 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(2566, 32640, F256, 6, 4) (dual of [(32640, 6), 195834, 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 (100, 112, 5657678)-net over F16 | [i] | Trace Code for Nets | |