Information on Result #2266837
Linear OA(3228, 6620, F3, 40) (dual of [6620, 6392, 41]-code), using 3 times code embedding in larger space based on linear OA(3225, 6617, F3, 40) (dual of [6617, 6392, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(31) [i] based on
- linear OA(3209, 6561, F3, 40) (dual of [6561, 6352, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3169, 6561, F3, 32) (dual of [6561, 6392, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(316, 56, F3, 7) (dual of [56, 40, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-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(3228, 5284, F3, 2, 40) (dual of [(5284, 2), 10340, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3228, 5284, F3, 3, 40) (dual of [(5284, 3), 15624, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(3228, 5284, F3, 4, 40) (dual of [(5284, 4), 20908, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3228, 5284, F3, 5, 40) (dual of [(5284, 5), 26192, 41]-NRT-code) | [i] | ||
| 5 | Digital (188, 228, 5284)-net over F3 | [i] | ||
| 6 | Linear OOA(3228, 1655, F3, 4, 40) (dual of [(1655, 4), 6392, 41]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3228, 1324, F3, 5, 40) (dual of [(1324, 5), 6392, 41]-NRT-code) | [i] | ||