Information on Result #1190460
Digital (42, 56, 687)-net over F7, using net defined by OOA based on linear OOA(756, 687, F7, 14, 14) (dual of [(687, 14), 9562, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(756, 4809, F7, 14) (dual of [4809, 4753, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(756, 4812, F7, 14) (dual of [4812, 4756, 15]-code), using
- trace code [i] based on linear OA(4928, 2406, F49, 14) (dual of [2406, 2378, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(4927, 2401, F49, 14) (dual of [2401, 2374, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(4923, 2401, F49, 12) (dual of [2401, 2378, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(491, 5, F49, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- trace code [i] based on linear OA(4928, 2406, F49, 14) (dual of [2406, 2378, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(756, 4812, F7, 14) (dual of [4812, 4756, 15]-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 (43, 57, 687)-net over F7 | [i] | Net Duplication | |