Information on Result #694739
Linear OA(2784, 531461, F27, 21) (dual of [531461, 531377, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2781, 531442, F27, 21) (dual of [531442, 531361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2765, 531442, F27, 17) (dual of [531442, 531377, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(273, 19, F27, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,27) or 19-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 OOA(2784, 531461, F27, 2, 21) (dual of [(531461, 2), 1062838, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (63, 84, 531461)-net over F27 | [i] | ||
| 3 | Linear OOA(2784, 265730, F27, 2, 21) (dual of [(265730, 2), 531376, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2784, 53146, F27, 21, 21) (dual of [(53146, 21), 1115982, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |