Information on Result #1190674
Digital (51, 68, 601)-net over F7, using net defined by OOA based on linear OOA(768, 601, F7, 17, 17) (dual of [(601, 17), 10149, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(768, 4809, F7, 17) (dual of [4809, 4741, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(768, 4814, F7, 17) (dual of [4814, 4746, 18]-code), using
- trace code [i] based on linear OA(4934, 2407, F49, 17) (dual of [2407, 2373, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(4933, 2402, F49, 17) (dual of [2402, 2369, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(4929, 2402, F49, 15) (dual of [2402, 2373, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2402 | 494−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [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 C([0,8]) ⊂ C([0,7]) [i] based on
- trace code [i] based on linear OA(4934, 2407, F49, 17) (dual of [2407, 2373, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(768, 4814, F7, 17) (dual of [4814, 4746, 18]-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 (52, 69, 601)-net over F7 | [i] | Net Duplication | |