Information on Result #698021
Linear OA(4918, 5764812, F49, 5) (dual of [5764812, 5764794, 6]-code), using construction X4 applied to C([0,2]) ⊂ C([0,1]) based on
- linear OA(4917, 5764802, F49, 5) (dual of [5764802, 5764785, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(499, 5764802, F49, 3) (dual of [5764802, 5764793, 4]-code or 5764802-cap in PG(8,49)), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(499, 10, F49, 9) (dual of [10, 1, 10]-code or 10-arc in PG(8,49)), using
- dual of repetition code with length 10 [i]
- linear OA(491, 10, F49, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-code), using
- Reed–Solomon code RS(48,49) [i]
- discarding factors / shortening the dual code based on linear OA(491, 49, F49, 1) (dual of [49, 48, 2]-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(4918, 5764812, F49, 2, 5) (dual of [(5764812, 2), 11529606, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4918, 5764812, F49, 3, 5) (dual of [(5764812, 3), 17294418, 6]-NRT-code) | [i] | ||
| 3 | Digital (13, 18, 5764812)-net over F49 | [i] | ||
| 4 | Linear OOA(4918, 2882406, F49, 2, 5) (dual of [(2882406, 2), 5764794, 6]-NRT-code) | [i] | OOA Folding | |