Information on Result #822711
Linear OOA(470, 2097162, F4, 2, 9) (dual of [(2097162, 2), 4194254, 10]-NRT-code), using OOA 2-folding based on linear OA(470, 4194324, F4, 9) (dual of [4194324, 4194254, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(470, 4194325, F4, 9) (dual of [4194325, 4194255, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(5) [i] based on
- linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(8) ⊂ Ce(5) [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 | Linear OOA(494, 4194324, F4, 2, 9) (dual of [(4194324, 2), 8388554, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(470, 2097162, F4, 3, 9) (dual of [(2097162, 3), 6291416, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (61, 70, 2097162)-net over F4 | [i] | ||