Information on Result #1179478
Digital (10, 14, 2403)-net over F7, using net defined by OOA based on linear OOA(714, 2403, F7, 4, 4) (dual of [(2403, 4), 9598, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(714, 2403, F7, 3, 4) (dual of [(2403, 3), 7195, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(714, 4806, F7, 4) (dual of [4806, 4792, 5]-code), using
- trace code [i] based on linear OA(497, 2403, F49, 4) (dual of [2403, 2396, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(497, 2401, F49, 4) (dual of [2401, 2394, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(495, 2401, F49, 3) (dual of [2401, 2396, 4]-code or 2401-cap in PG(4,49)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- trace code [i] based on linear OA(497, 2403, F49, 4) (dual of [2403, 2396, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(714, 4806, F7, 4) (dual of [4806, 4792, 5]-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 (71, 80, 2884805)-net over F7 | [i] | (u, u+v)-Construction for Nets | |