Information on Result #675173
Linear OA(3207, 19718, F3, 34) (dual of [19718, 19511, 35]-code), using construction X applied to Ce(33) ⊂ Ce(28) based on
- linear OA(3199, 19683, F3, 34) (dual of [19683, 19484, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [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(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(3208, 19719, F3, 34) (dual of [19719, 19511, 35]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3206, 19717, F3, 33) (dual of [19717, 19511, 34]-code) | [i] | Truncation | |
| 3 | Linear OOA(3207, 9859, F3, 2, 34) (dual of [(9859, 2), 19511, 35]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3207, 6572, F3, 3, 34) (dual of [(6572, 3), 19509, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(3207, 4929, F3, 4, 34) (dual of [(4929, 4), 19509, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(3207, 3943, F3, 5, 34) (dual of [(3943, 5), 19508, 35]-NRT-code) | [i] | ||