Information on Result #1190056
Digital (49, 59, 164712)-net over F7, using net defined by OOA based on linear OOA(759, 164712, F7, 10, 10) (dual of [(164712, 10), 1647061, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(759, 823560, F7, 10) (dual of [823560, 823501, 11]-code), using
- 1 times code embedding in larger space [i] based on linear OA(758, 823559, F7, 10) (dual of [823559, 823501, 11]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(9) ⊂ Ce(7) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(758, 823559, F7, 10) (dual of [823559, 823501, 11]-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 (50, 60, 164712)-net over F7 | [i] | Net Duplication | |