Information on Result #1186490
Digital (108, 123, 599189)-net over F4, using net defined by OOA based on linear OOA(4123, 599189, F4, 15, 15) (dual of [(599189, 15), 8987712, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(4123, 4194324, F4, 15) (dual of [4194324, 4194201, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 4194327, F4, 15) (dual of [4194327, 4194204, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(14) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(4123, 4194327, F4, 15) (dual of [4194327, 4194204, 16]-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 (109, 124, 599189)-net over F4 | [i] | Net Duplication | |
| 2 | Digital (110, 125, 599189)-net over F4 | [i] | ||
| 3 | Digital (116, 131, 599198)-net over F4 | [i] | (u, u+v)-Construction for Nets | |