Information on Result #695172
Linear OA(2794, 19698, F27, 32) (dual of [19698, 19604, 33]-code), using construction X applied to Ce(31) ⊂ Ce(27) based on
- linear OA(2791, 19683, F27, 32) (dual of [19683, 19592, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2779, 19683, F27, 28) (dual of [19683, 19604, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(273, 15, F27, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,27) or 15-cap in PG(2,27)), using
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), using
- Reed–Solomon code RS(24,27) [i]
- discarding factors / shortening the dual code based on linear OA(273, 27, F27, 3) (dual of [27, 24, 4]-code or 27-arc in PG(2,27) or 27-cap in PG(2,27)), 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(2795, 19699, F27, 32) (dual of [19699, 19604, 33]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(2794, 12663, F27, 2, 32) (dual of [(12663, 2), 25232, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (62, 94, 12663)-net over F27 | [i] | ||
| 4 | Linear OOA(2794, 9849, F27, 2, 32) (dual of [(9849, 2), 19604, 33]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2794, 1231, F27, 32, 32) (dual of [(1231, 32), 39298, 33]-NRT-code) | [i] | OA Folding and Stacking | |