Information on Result #736966
Linear OA(3204, 6605, F3, 37) (dual of [6605, 6401, 38]-code), using construction X applied to C([0,18]) ⊂ C([0,15]) based on
- linear OA(3193, 6562, F3, 37) (dual of [6562, 6369, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(3161, 6562, F3, 31) (dual of [6562, 6401, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 316−1, defining interval I = [0,15], and minimum distance d ≥ |{−15,−14,…,15}|+1 = 32 (BCH-bound) [i]
- linear OA(311, 43, F3, 5) (dual of [43, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-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(3204, 6605, F3, 36) (dual of [6605, 6401, 37]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3206, 6607, F3, 37) (dual of [6607, 6401, 38]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(3207, 6608, F3, 37) (dual of [6608, 6401, 38]-code) | [i] | ||
| 4 | Linear OA(3208, 6609, F3, 37) (dual of [6609, 6401, 38]-code) | [i] | ||
| 5 | Linear OA(3203, 6604, F3, 36) (dual of [6604, 6401, 37]-code) | [i] | Truncation | |
| 6 | Linear OA(3208, 6610, F3, 37) (dual of [6610, 6402, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(3204, 3302, F3, 2, 37) (dual of [(3302, 2), 6400, 38]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3204, 1651, F3, 4, 37) (dual of [(1651, 4), 6400, 38]-NRT-code) | [i] | ||
| 9 | Linear OOA(3204, 1321, F3, 5, 37) (dual of [(1321, 5), 6401, 38]-NRT-code) | [i] | ||