Information on Result #1188332
Digital (43, 51, 97661)-net over F5, using net defined by OOA based on linear OOA(551, 97661, F5, 8, 8) (dual of [(97661, 8), 781237, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(551, 390644, F5, 8) (dual of [390644, 390593, 9]-code), using
- 1 times code embedding in larger space [i] based on linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-code), using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(549, 390625, F5, 8) (dual of [390625, 390576, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(517, 18, F5, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,5)), using
- dual of repetition code with length 18 [i]
- linear OA(51, 18, F5, 1) (dual of [18, 17, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(7) ⊂ Ce(5) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(550, 390643, F5, 8) (dual of [390643, 390593, 9]-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 (44, 52, 97661)-net over F5 | [i] | Net Duplication | |