Information on Result #675169
Linear OA(3225, 19718, F3, 37) (dual of [19718, 19493, 38]-code), using construction X applied to Ce(36) ⊂ Ce(31) 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(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(38, 35, F3, 4) (dual of [35, 27, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-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(3226, 19719, F3, 37) (dual of [19719, 19493, 38]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3224, 19717, F3, 36) (dual of [19717, 19493, 37]-code) | [i] | Truncation | |
| 3 | Linear OOA(3225, 9859, F3, 2, 37) (dual of [(9859, 2), 19493, 38]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3225, 6572, F3, 3, 37) (dual of [(6572, 3), 19491, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(3225, 4929, F3, 4, 37) (dual of [(4929, 4), 19491, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(3225, 3943, F3, 5, 37) (dual of [(3943, 5), 19490, 38]-NRT-code) | [i] | ||