Information on Result #737020
Linear OA(3184, 6616, F3, 32) (dual of [6616, 6432, 33]-code), using construction X applied to Ce(31) ⊂ Ce(24) based on
- 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(3129, 6561, F3, 25) (dual of [6561, 6432, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-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 OA(3186, 6618, F3, 32) (dual of [6618, 6432, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3187, 6619, F3, 32) (dual of [6619, 6432, 33]-code) | [i] | ||
| 3 | Linear OA(3188, 6620, F3, 32) (dual of [6620, 6432, 33]-code) | [i] | ||
| 4 | Linear OOA(3184, 4871, F3, 2, 32) (dual of [(4871, 2), 9558, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(3184, 4871, F3, 3, 32) (dual of [(4871, 3), 14429, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(3184, 4871, F3, 4, 32) (dual of [(4871, 4), 19300, 33]-NRT-code) | [i] | ||
| 7 | Linear OOA(3184, 4871, F3, 5, 32) (dual of [(4871, 5), 24171, 33]-NRT-code) | [i] | ||
| 8 | Digital (152, 184, 4871)-net over F3 | [i] | ||
| 9 | Linear OA(3188, 6622, F3, 32) (dual of [6622, 6434, 33]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OOA(3184, 3308, F3, 2, 32) (dual of [(3308, 2), 6432, 33]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(3184, 2205, F3, 3, 32) (dual of [(2205, 3), 6431, 33]-NRT-code) | [i] | ||
| 12 | Linear OOA(3184, 1654, F3, 4, 32) (dual of [(1654, 4), 6432, 33]-NRT-code) | [i] | ||
| 13 | Linear OOA(3184, 1323, F3, 5, 32) (dual of [(1323, 5), 6431, 33]-NRT-code) | [i] | ||