Information on Result #695116
Linear OA(2789, 19690, F27, 31) (dual of [19690, 19601, 32]-code), using construction X applied to Ce(30) ⊂ Ce(28) based on
- linear OA(2788, 19683, F27, 31) (dual of [19683, 19595, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2782, 19683, F27, 29) (dual of [19683, 19601, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(271, 7, F27, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 | OA(9134, 19690, S9, 31) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(27109, 19772, S27, 31) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(2789, 9885, F27, 2, 31) (dual of [(9885, 2), 19681, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (58, 89, 9885)-net over F27 | [i] | ||
| 5 | Linear OOA(2789, 9845, F27, 2, 31) (dual of [(9845, 2), 19601, 32]-NRT-code) | [i] | OOA Folding | |