Information on Result #2266679
Linear OA(3212, 6620, F3, 37) (dual of [6620, 6408, 38]-code), using 3 times code embedding in larger space based on linear OA(3209, 6617, F3, 37) (dual of [6617, 6408, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(28) [i] 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 OOA(3212, 5198, F3, 2, 37) (dual of [(5198, 2), 10184, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3212, 5198, F3, 3, 37) (dual of [(5198, 3), 15382, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(3212, 5198, F3, 4, 37) (dual of [(5198, 4), 20580, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(3212, 5198, F3, 5, 37) (dual of [(5198, 5), 25778, 38]-NRT-code) | [i] | ||
| 5 | Digital (175, 212, 5198)-net over F3 | [i] | ||
| 6 | Linear OOA(3212, 1655, F3, 4, 37) (dual of [(1655, 4), 6408, 38]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3212, 1324, F3, 5, 37) (dual of [(1324, 5), 6408, 38]-NRT-code) | [i] | ||