Information on Result #1190288
Digital (56, 68, 39217)-net over F7, using net defined by OOA based on linear OOA(768, 39217, F7, 12, 12) (dual of [(39217, 12), 470536, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(768, 235302, F7, 12) (dual of [235302, 235234, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(768, 235304, F7, 12) (dual of [235304, 235236, 13]-code), using
- trace code [i] based on linear OA(4934, 117652, F49, 12) (dual of [117652, 117618, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(4934, 117649, F49, 12) (dual of [117649, 117615, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4931, 117649, F49, 11) (dual of [117649, 117618, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 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(11) ⊂ Ce(10) [i] based on
- trace code [i] based on linear OA(4934, 117652, F49, 12) (dual of [117652, 117618, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(768, 235304, F7, 12) (dual of [235304, 235236, 13]-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 (57, 69, 39217)-net over F7 | [i] | Net Duplication | |