Information on Result #675246
Linear OA(3229, 19758, F3, 35) (dual of [19758, 19529, 36]-code), using construction X applied to Ce(34) ⊂ Ce(25) 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(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(321, 75, F3, 8) (dual of [75, 54, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(321, 80, F3, 8) (dual of [80, 59, 9]-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(3230, 19759, F3, 35) (dual of [19759, 19529, 36]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(3229, 12994, F3, 2, 35) (dual of [(12994, 2), 25759, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(3229, 12994, F3, 3, 35) (dual of [(12994, 3), 38753, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(3229, 12994, F3, 4, 35) (dual of [(12994, 4), 51747, 36]-NRT-code) | [i] | ||
| 5 | Linear OOA(3229, 12994, F3, 5, 35) (dual of [(12994, 5), 64741, 36]-NRT-code) | [i] | ||
| 6 | Digital (194, 229, 12994)-net over F3 | [i] | ||
| 7 | Linear OOA(3229, 9879, F3, 2, 35) (dual of [(9879, 2), 19529, 36]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(3229, 6586, F3, 3, 35) (dual of [(6586, 3), 19529, 36]-NRT-code) | [i] | ||
| 9 | Linear OOA(3229, 4939, F3, 4, 35) (dual of [(4939, 4), 19527, 36]-NRT-code) | [i] | ||
| 10 | Linear OOA(3229, 3951, F3, 5, 35) (dual of [(3951, 5), 19526, 36]-NRT-code) | [i] | ||