Information on Result #1190324
Digital (82, 94, 1921604)-net over F7, using net defined by OOA based on linear OOA(794, 1921604, F7, 14, 12) (dual of [(1921604, 14), 26902362, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(794, 5764813, F7, 2, 12) (dual of [(5764813, 2), 11529532, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(794, 5764814, F7, 2, 12) (dual of [(5764814, 2), 11529534, 13]-NRT-code), using
- trace code [i] based on linear OOA(4947, 2882407, F49, 2, 12) (dual of [(2882407, 2), 5764767, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4947, 5764814, F49, 12) (dual of [5764814, 5764767, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(4947, 5764815, F49, 12) (dual of [5764815, 5764768, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(4933, 5764801, F49, 9) (dual of [5764801, 5764768, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(492, 14, F49, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(11) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(4947, 5764815, F49, 12) (dual of [5764815, 5764768, 13]-code), using
- OOA 2-folding [i] based on linear OA(4947, 5764814, F49, 12) (dual of [5764814, 5764767, 13]-code), using
- trace code [i] based on linear OOA(4947, 2882407, F49, 2, 12) (dual of [(2882407, 2), 5764767, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(794, 5764814, F7, 2, 12) (dual of [(5764814, 2), 11529534, 13]-NRT-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 (83, 95, 1921604)-net over F7 | [i] | Net Duplication | |