Information on Result #695144
Linear OA(2782, 19695, F27, 28) (dual of [19695, 19613, 29]-code), using construction X applied to Ce(27) ⊂ Ce(23) based on
- 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(2770, 19683, F27, 24) (dual of [19683, 19613, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(273, 12, F27, 3) (dual of [12, 9, 4]-code or 12-arc in PG(2,27) or 12-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(2781, 19694, F27, 27) (dual of [19694, 19613, 28]-code) | [i] | Truncation | |
| 2 | Linear OOA(2782, 11670, F27, 2, 28) (dual of [(11670, 2), 23258, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (54, 82, 11670)-net over F27 | [i] | ||
| 4 | Linear OOA(2782, 9847, F27, 2, 28) (dual of [(9847, 2), 19612, 29]-NRT-code) | [i] | OOA Folding | |