Information on Result #694968
Linear OA(2750, 19691, F27, 17) (dual of [19691, 19641, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,7]) based on
- linear OA(2749, 19684, F27, 17) (dual of [19684, 19635, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2743, 19684, F27, 15) (dual of [19684, 19641, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 276−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [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(975, 19691, S9, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OA(2760, 19739, F27, 17) (dual of [19739, 19679, 18]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(2762, 19755, F27, 17) (dual of [19755, 19693, 18]-code) | [i] | ||
| 4 | OA(2762, 19791, S27, 17) | [i] | ||
| 5 | Linear OOA(2750, 11704, F27, 2, 17) (dual of [(11704, 2), 23358, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (33, 50, 11704)-net over F27 | [i] | ||
| 7 | Linear OOA(2750, 9845, F27, 2, 17) (dual of [(9845, 2), 19640, 18]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2750, 2461, F27, 17, 17) (dual of [(2461, 17), 41787, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |