Information on Result #675243
Linear OA(3247, 19758, F3, 38) (dual of [19758, 19511, 39]-code), using construction X applied to Ce(37) ⊂ Ce(28) based on
- linear OA(3226, 19683, F3, 38) (dual of [19683, 19457, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3172, 19683, F3, 29) (dual of [19683, 19511, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(3248, 19759, F3, 38) (dual of [19759, 19511, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3249, 19760, F3, 38) (dual of [19760, 19511, 39]-code) | [i] | ||
| 3 | Linear OOA(3247, 12968, F3, 2, 38) (dual of [(12968, 2), 25689, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3247, 12968, F3, 3, 38) (dual of [(12968, 3), 38657, 39]-NRT-code) | [i] | ||
| 5 | Linear OOA(3247, 12968, F3, 4, 38) (dual of [(12968, 4), 51625, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(3247, 12968, F3, 5, 38) (dual of [(12968, 5), 64593, 39]-NRT-code) | [i] | ||
| 7 | Digital (209, 247, 12968)-net over F3 | [i] | ||
| 8 | Linear OOA(3247, 9879, F3, 2, 38) (dual of [(9879, 2), 19511, 39]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(3247, 6586, F3, 3, 38) (dual of [(6586, 3), 19511, 39]-NRT-code) | [i] | ||
| 10 | Linear OOA(3247, 4939, F3, 4, 38) (dual of [(4939, 4), 19509, 39]-NRT-code) | [i] | ||
| 11 | Linear OOA(3247, 3951, F3, 5, 38) (dual of [(3951, 5), 19508, 39]-NRT-code) | [i] | ||