Information on Result #2266379
Linear OA(3210, 19748, F3, 32) (dual of [19748, 19538, 33]-code), using 5 times code embedding in larger space based on linear OA(3205, 19743, F3, 32) (dual of [19743, 19538, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3190, 19683, F3, 32) (dual of [19683, 19493, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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 OOA(3210, 12668, F3, 2, 32) (dual of [(12668, 2), 25126, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3210, 12668, F3, 3, 32) (dual of [(12668, 3), 37794, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(3210, 12668, F3, 4, 32) (dual of [(12668, 4), 50462, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(3210, 12668, F3, 5, 32) (dual of [(12668, 5), 63130, 33]-NRT-code) | [i] | ||
| 5 | Digital (178, 210, 12668)-net over F3 | [i] | ||