Information on Result #675457
Linear OA(3213, 6581, F3, 40) (dual of [6581, 6368, 41]-code), using construction X applied to Ce(39) ⊂ Ce(36) 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(3193, 6561, F3, 37) (dual of [6561, 6368, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(34, 20, F3, 2) (dual of [20, 16, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 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 OA(3214, 6582, F3, 40) (dual of [6582, 6368, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3213, 3412, F3, 2, 40) (dual of [(3412, 2), 6611, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3213, 3412, F3, 3, 40) (dual of [(3412, 3), 10023, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(3213, 3412, F3, 4, 40) (dual of [(3412, 4), 13435, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(3213, 3412, F3, 5, 40) (dual of [(3412, 5), 16847, 41]-NRT-code) | [i] | ||
| 6 | Digital (173, 213, 3412)-net over F3 | [i] | ||
| 7 | Linear OOA(3213, 3290, F3, 2, 40) (dual of [(3290, 2), 6367, 41]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3213, 2193, F3, 3, 40) (dual of [(2193, 3), 6366, 41]-NRT-code) | [i] | ||
| 9 | Linear OOA(3213, 1645, F3, 4, 40) (dual of [(1645, 4), 6367, 41]-NRT-code) | [i] | ||
| 10 | Linear OOA(3213, 1316, F3, 5, 40) (dual of [(1316, 5), 6367, 41]-NRT-code) | [i] | ||