Information on Result #736945
Linear OA(3223, 19743, F3, 35) (dual of [19743, 19520, 36]-code), using construction X applied to Ce(34) ⊂ Ce(27) based on
- linear OA(3208, 19683, F3, 35) (dual of [19683, 19475, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(3163, 19683, F3, 28) (dual of [19683, 19520, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(315, 60, F3, 6) (dual of [60, 45, 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(3225, 19745, F3, 35) (dual of [19745, 19520, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3226, 19746, F3, 35) (dual of [19746, 19520, 36]-code) | [i] | ||
| 3 | Linear OA(3227, 19747, F3, 35) (dual of [19747, 19520, 36]-code) | [i] | ||
| 4 | Linear OA(3228, 19748, F3, 35) (dual of [19748, 19520, 36]-code) | [i] | ||
| 5 | Linear OA(3227, 19748, F3, 35) (dual of [19748, 19521, 36]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(3223, 9871, F3, 2, 35) (dual of [(9871, 2), 19519, 36]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(3223, 6581, F3, 3, 35) (dual of [(6581, 3), 19520, 36]-NRT-code) | [i] | ||
| 8 | Linear OOA(3223, 4935, F3, 4, 35) (dual of [(4935, 4), 19517, 36]-NRT-code) | [i] | ||
| 9 | Linear OOA(3223, 3948, F3, 5, 35) (dual of [(3948, 5), 19517, 36]-NRT-code) | [i] | ||