Information on Result #737013
Linear OA(3209, 6617, F3, 37) (dual of [6617, 6408, 38]-code), using construction X applied to Ce(36) ⊂ Ce(28) based on
- 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(3153, 6561, F3, 29) (dual of [6561, 6408, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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 OA(3211, 6619, F3, 37) (dual of [6619, 6408, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3212, 6620, F3, 37) (dual of [6620, 6408, 38]-code) | [i] | ||
| 3 | Linear OA(3213, 6621, F3, 37) (dual of [6621, 6408, 38]-code) | [i] | ||
| 4 | Linear OA(3208, 6616, F3, 36) (dual of [6616, 6408, 37]-code) | [i] | Truncation | |
| 5 | Linear OOA(3209, 4728, F3, 2, 37) (dual of [(4728, 2), 9247, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3209, 4728, F3, 3, 37) (dual of [(4728, 3), 13975, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(3209, 4728, F3, 4, 37) (dual of [(4728, 4), 18703, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(3209, 4728, F3, 5, 37) (dual of [(4728, 5), 23431, 38]-NRT-code) | [i] | ||
| 9 | Digital (172, 209, 4728)-net over F3 | [i] | ||
| 10 | Linear OA(3212, 6621, F3, 37) (dual of [6621, 6409, 38]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OA(3213, 6623, F3, 37) (dual of [6623, 6410, 38]-code) | [i] | ||
| 12 | Linear OOA(3209, 3308, F3, 2, 37) (dual of [(3308, 2), 6407, 38]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(3209, 2205, F3, 3, 37) (dual of [(2205, 3), 6406, 38]-NRT-code) | [i] | ||
| 14 | Linear OOA(3209, 1654, F3, 4, 37) (dual of [(1654, 4), 6407, 38]-NRT-code) | [i] | ||
| 15 | Linear OOA(3209, 1323, F3, 5, 37) (dual of [(1323, 5), 6406, 38]-NRT-code) | [i] | ||