Information on Result #737029
Linear OA(3241, 6625, F3, 42) (dual of [6625, 6384, 43]-code), using construction X applied to Ce(42) ⊂ Ce(33) based on
- linear OA(3225, 6561, F3, 43) (dual of [6561, 6336, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3177, 6561, F3, 34) (dual of [6561, 6384, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(316, 64, F3, 7) (dual of [64, 48, 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 OA(3243, 6627, F3, 42) (dual of [6627, 6384, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3244, 6628, F3, 42) (dual of [6628, 6384, 43]-code) | [i] | ||
| 3 | Linear OOA(3241, 5709, F3, 2, 42) (dual of [(5709, 2), 11177, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3241, 5709, F3, 3, 42) (dual of [(5709, 3), 16886, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(3241, 5709, F3, 4, 42) (dual of [(5709, 4), 22595, 43]-NRT-code) | [i] | ||
| 6 | Linear OOA(3241, 5709, F3, 5, 42) (dual of [(5709, 5), 28304, 43]-NRT-code) | [i] | ||
| 7 | Digital (199, 241, 5709)-net over F3 | [i] | ||
| 8 | Linear OA(3243, 6628, F3, 42) (dual of [6628, 6385, 43]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3244, 6630, F3, 42) (dual of [6630, 6386, 43]-code) | [i] | ||
| 10 | Linear OA(3245, 6632, F3, 42) (dual of [6632, 6387, 43]-code) | [i] | ||
| 11 | Linear OA(3246, 6634, F3, 42) (dual of [6634, 6388, 43]-code) | [i] | ||
| 12 | Linear OA(3247, 6636, F3, 42) (dual of [6636, 6389, 43]-code) | [i] | ||
| 13 | Linear OA(3248, 6638, F3, 42) (dual of [6638, 6390, 43]-code) | [i] | ||
| 14 | Linear OOA(3241, 3312, F3, 2, 42) (dual of [(3312, 2), 6383, 43]-NRT-code) | [i] | OOA Folding | |
| 15 | Linear OOA(3241, 2208, F3, 3, 42) (dual of [(2208, 3), 6383, 43]-NRT-code) | [i] | ||
| 16 | Linear OOA(3241, 1656, F3, 4, 42) (dual of [(1656, 4), 6383, 43]-NRT-code) | [i] | ||
| 17 | Linear OOA(3241, 1325, F3, 5, 42) (dual of [(1325, 5), 6384, 43]-NRT-code) | [i] | ||