Information on Result #694754
Linear OA(2786, 531470, F27, 21) (dual of [531470, 531384, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,7]) 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(2757, 531442, F27, 15) (dual of [531442, 531385, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(275, 28, F27, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
- extended Reed–Solomon code RSe(23,27) [i]
- the expurgated narrow-sense BCH-code C(I) with length 28 | 272−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
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(2786, 531470, F27, 2, 21) (dual of [(531470, 2), 1062854, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (65, 86, 531470)-net over F27 | [i] | ||
| 3 | Linear OOA(2786, 265735, F27, 2, 21) (dual of [(265735, 2), 531384, 22]-NRT-code) | [i] | OOA Folding | |