Information on Result #698025
Linear OA(4954, 5764831, F49, 13) (dual of [5764831, 5764777, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,3]) based on
- linear OA(4949, 5764802, F49, 13) (dual of [5764802, 5764753, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4925, 5764802, F49, 7) (dual of [5764802, 5764777, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(495, 29, F49, 5) (dual of [29, 24, 6]-code or 29-arc in PG(4,49)), using
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), using
- Reed–Solomon code RS(44,49) [i]
- discarding factors / shortening the dual code based on linear OA(495, 49, F49, 5) (dual of [49, 44, 6]-code or 49-arc in PG(4,49)), 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(4954, 5764831, F49, 2, 13) (dual of [(5764831, 2), 11529608, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4954, 5764831, F49, 3, 13) (dual of [(5764831, 3), 17294439, 14]-NRT-code) | [i] | ||
| 3 | Digital (41, 54, 5764831)-net over F49 | [i] | ||
| 4 | Linear OOA(4954, 2882415, F49, 2, 13) (dual of [(2882415, 2), 5764776, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4954, 1921610, F49, 3, 13) (dual of [(1921610, 3), 5764776, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(4954, 960805, F49, 13, 13) (dual of [(960805, 13), 12490411, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |