Information on Result #698022
Linear OA(4952, 5764821, F49, 13) (dual of [5764821, 5764769, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,4]) 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(4933, 5764802, F49, 9) (dual of [5764802, 5764769, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 5764802 | 498−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(493, 19, F49, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,49) or 19-cap in PG(2,49)), using
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), using
- Reed–Solomon code RS(46,49) [i]
- discarding factors / shortening the dual code based on linear OA(493, 49, F49, 3) (dual of [49, 46, 4]-code or 49-arc in PG(2,49) or 49-cap in PG(2,49)), 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(4952, 5764821, F49, 2, 13) (dual of [(5764821, 2), 11529590, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4952, 5764821, F49, 3, 13) (dual of [(5764821, 3), 17294411, 14]-NRT-code) | [i] | ||
| 3 | Digital (39, 52, 5764821)-net over F49 | [i] | ||
| 4 | Linear OOA(4952, 2882410, F49, 2, 13) (dual of [(2882410, 2), 5764768, 14]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(4952, 1921607, F49, 3, 13) (dual of [(1921607, 3), 5764769, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(4952, 960803, F49, 13, 13) (dual of [(960803, 13), 12490387, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |