Information on Result #2272750
Linear OA(4187, 65578, F4, 30) (dual of [65578, 65391, 31]-code), using 3 times code embedding in larger space based on linear OA(4184, 65575, F4, 30) (dual of [65575, 65391, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-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(4187, 37586, F4, 2, 30) (dual of [(37586, 2), 74985, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4187, 37586, F4, 3, 30) (dual of [(37586, 3), 112571, 31]-NRT-code) | [i] | ||
| 3 | Digital (157, 187, 37586)-net over F4 | [i] | ||