Information on Result #694760
Linear OA(2770, 531470, F27, 17) (dual of [531470, 531400, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,5]) based on
- 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(2741, 531442, F27, 11) (dual of [531442, 531401, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 278−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (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(2770, 531470, F27, 2, 17) (dual of [(531470, 2), 1062870, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 70, 531470)-net over F27 | [i] | ||
| 3 | Linear OOA(2770, 265735, F27, 2, 17) (dual of [(265735, 2), 531400, 18]-NRT-code) | [i] | OOA Folding | |