Information on Result #737016
Linear OA(3200, 6616, F3, 35) (dual of [6616, 6416, 36]-code), using construction X applied to Ce(34) ⊂ Ce(27) based on
- linear OA(3185, 6561, F3, 35) (dual of [6561, 6376, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3145, 6561, F3, 28) (dual of [6561, 6416, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 55, F3, 6) (dual of [55, 40, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-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(3202, 6618, F3, 35) (dual of [6618, 6416, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3203, 6619, F3, 35) (dual of [6619, 6416, 36]-code) | [i] | ||
| 3 | Linear OA(3204, 6620, F3, 35) (dual of [6620, 6416, 36]-code) | [i] | ||
| 4 | Linear OA(3205, 6621, F3, 35) (dual of [6621, 6416, 36]-code) | [i] | ||
| 5 | Linear OOA(3200, 4929, F3, 2, 35) (dual of [(4929, 2), 9658, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(3200, 4929, F3, 3, 35) (dual of [(4929, 3), 14587, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(3200, 4929, F3, 4, 35) (dual of [(4929, 4), 19516, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(3200, 4929, F3, 5, 35) (dual of [(4929, 5), 24445, 36]-NRT-code) | [i] | ||
| 9 | Digital (165, 200, 4929)-net over F3 | [i] | ||
| 10 | Linear OA(3204, 6622, F3, 35) (dual of [6622, 6418, 36]-code) | [i] | Construction X with Varšamov Bound | |
| 11 | Linear OOA(3200, 3308, F3, 2, 35) (dual of [(3308, 2), 6416, 36]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(3200, 2205, F3, 3, 35) (dual of [(2205, 3), 6415, 36]-NRT-code) | [i] | ||
| 13 | Linear OOA(3200, 1654, F3, 4, 35) (dual of [(1654, 4), 6416, 36]-NRT-code) | [i] | ||
| 14 | Linear OOA(3200, 1323, F3, 5, 35) (dual of [(1323, 5), 6415, 36]-NRT-code) | [i] | ||