Information on Result #822712
Linear OOA(471, 2097165, F4, 2, 9) (dual of [(2097165, 2), 4194259, 10]-NRT-code), using OOA 2-folding based on linear OA(471, 4194330, F4, 9) (dual of [4194330, 4194259, 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(44, 26, F4, 2) (dual of [26, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
- Hamming code H(4,4) [i]
- discarding factors / shortening the dual code based on linear OA(44, 85, F4, 2) (dual of [85, 81, 3]-code), using
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(495, 4194330, F4, 2, 9) (dual of [(4194330, 2), 8388565, 10]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(471, 2097165, F4, 3, 9) (dual of [(2097165, 3), 6291424, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (62, 71, 2097165)-net over F4 | [i] | ||