Information on Result #675181
Linear OA(3171, 19718, F3, 28) (dual of [19718, 19547, 29]-code), using construction X applied to Ce(27) ⊂ Ce(22) based on
- 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(3136, 19683, F3, 23) (dual of [19683, 19547, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(3172, 19719, F3, 28) (dual of [19719, 19547, 29]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3170, 19717, F3, 27) (dual of [19717, 19547, 28]-code) | [i] | Truncation | |
| 3 | Linear OOA(3171, 9859, F3, 2, 28) (dual of [(9859, 2), 19547, 29]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3171, 6572, F3, 3, 28) (dual of [(6572, 3), 19545, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(3171, 4929, F3, 4, 28) (dual of [(4929, 4), 19545, 29]-NRT-code) | [i] | ||
| 6 | Linear OOA(3171, 3943, F3, 5, 28) (dual of [(3943, 5), 19544, 29]-NRT-code) | [i] | ||
| 7 | Linear OOA(3171, 1408, F3, 28, 28) (dual of [(1408, 28), 39253, 29]-NRT-code) | [i] | OA Folding and Stacking | |