Information on Result #1204504
Digital (35, 47, 1419947)-net over F256, using net defined by OOA based on linear OOA(25647, 1419947, F256, 18, 12) (dual of [(1419947, 18), 25558999, 13]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(25647, 1419948, F256, 6, 12) (dual of [(1419948, 6), 8519641, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25613, 21848, F256, 6, 6) (dual of [(21848, 6), 131075, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2565, 65536, F256, 3) (dual of [65536, 65531, 4]-code or 65536-cap in PG(4,256)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(5) ⊂ Ce(2) [i] based on
- OA 3-folding and stacking [i] based on linear OA(25613, 65544, F256, 6) (dual of [65544, 65531, 7]-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(25613, 21848, F256, 6, 6) (dual of [(21848, 6), 131075, 7]-NRT-code), using
- (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 (176, 188, 5679788)-net over F4 | [i] | Trace Code for Nets | |
| 2 | Digital (82, 94, 2839894)-net over F16 | [i] | ||