Information on Result #675193
Linear OA(3117, 19718, F3, 19) (dual of [19718, 19601, 20]-code), using construction X applied to Ce(18) ⊂ Ce(13) based on
- linear OA(3109, 19683, F3, 19) (dual of [19683, 19574, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(382, 19683, F3, 14) (dual of [19683, 19601, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(3118, 19719, F3, 19) (dual of [19719, 19601, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3116, 19717, F3, 18) (dual of [19717, 19601, 19]-code) | [i] | Truncation | |
| 3 | Linear OOA(3117, 9859, F3, 2, 19) (dual of [(9859, 2), 19601, 20]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3117, 6572, F3, 3, 19) (dual of [(6572, 3), 19599, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(3117, 4929, F3, 4, 19) (dual of [(4929, 4), 19599, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(3117, 3943, F3, 5, 19) (dual of [(3943, 5), 19598, 20]-NRT-code) | [i] | ||