Information on Result #736960
Linear OA(3233, 19753, F3, 36) (dual of [19753, 19520, 37]-code), using construction X applied to Ce(36) ⊂ Ce(27) based on
- linear OA(3217, 19683, F3, 37) (dual of [19683, 19466, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(316, 70, F3, 7) (dual of [70, 54, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(316, 82, F3, 7) (dual of [82, 66, 8]-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(3235, 19755, F3, 36) (dual of [19755, 19520, 37]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3236, 19756, F3, 36) (dual of [19756, 19520, 37]-code) | [i] | ||
| 3 | Linear OOA(3233, 12160, F3, 2, 36) (dual of [(12160, 2), 24087, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(3233, 12160, F3, 3, 36) (dual of [(12160, 3), 36247, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(3233, 12160, F3, 4, 36) (dual of [(12160, 4), 48407, 37]-NRT-code) | [i] | ||
| 6 | Linear OOA(3233, 12160, F3, 5, 36) (dual of [(12160, 5), 60567, 37]-NRT-code) | [i] | ||
| 7 | Digital (197, 233, 12160)-net over F3 | [i] | ||
| 8 | Linear OA(3237, 19758, F3, 36) (dual of [19758, 19521, 37]-code) | [i] | Construction X with Varšamov Bound | |
| 9 | Linear OA(3239, 19761, F3, 36) (dual of [19761, 19522, 37]-code) | [i] | ||
| 10 | Linear OOA(3233, 9876, F3, 2, 36) (dual of [(9876, 2), 19519, 37]-NRT-code) | [i] | OOA Folding | |
| 11 | Linear OOA(3233, 6584, F3, 3, 36) (dual of [(6584, 3), 19519, 37]-NRT-code) | [i] | ||
| 12 | Linear OOA(3233, 4938, F3, 4, 36) (dual of [(4938, 4), 19519, 37]-NRT-code) | [i] | ||
| 13 | Linear OOA(3233, 3950, F3, 5, 36) (dual of [(3950, 5), 19517, 37]-NRT-code) | [i] | ||