Information on Result #962132
Linear OOA(4180, 1398108, F4, 3, 22) (dual of [(1398108, 3), 4194144, 23]-NRT-code), using OOA 3-folding based on linear OA(4180, 4194324, F4, 22) (dual of [4194324, 4194144, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4180, 4194325, F4, 22) (dual of [4194325, 4194145, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(18) [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(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(21) ⊂ Ce(18) [i] based on
Mode: Constructive and 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 | Digital (158, 180, 1398108)-net over F4 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |