Information on Result #666639
Linear OA(2712, 2812, F27, 5) (dual of [2812, 2800, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(271, 703, F27, 1) (dual of [703, 702, 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
- linear OA(271, 703, F27, 1) (dual of [703, 702, 2]-code) (see above)
- linear OA(273, 703, F27, 2) (dual of [703, 700, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(273, 728, F27, 2) (dual of [728, 725, 3]-code), using
- linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-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 OOA(2712, 2812, F27, 2, 5) (dual of [(2812, 2), 5612, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (7, 12, 2812)-net over F27 | [i] | ||
| 3 | Linear OOA(2712, 1406, F27, 2, 5) (dual of [(1406, 2), 2800, 6]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2712, 1405, F27, 5, 5) (dual of [(1405, 5), 7013, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |