Information on Result #1364927
Linear OOA(4192, 2097192, F4, 2, 22) (dual of [(2097192, 2), 4194192, 23]-NRT-code), using OOA 2-folding based on linear OA(4192, 4194384, F4, 22) (dual of [4194384, 4194192, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4192, 4194385, F4, 22) (dual of [4194385, 4194193, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(415, 81, F4, 7) (dual of [81, 66, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(415, 85, F4, 7) (dual of [85, 70, 8]-code), using
- construction X applied to Ce(21) ⊂ Ce(13) [i] based on
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(4192, 2097192, F4, 3, 22) (dual of [(2097192, 3), 6291384, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (170, 192, 2097192)-net over F4 | [i] | ||