Information on Result #698024

Linear OA(4936, 5764821, F49, 9) (dual of [5764821, 5764785, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
  1. 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]
  2. 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]
  3. 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

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:

ResultThis
result
only		Method
1Linear OOA(4936, 5764821, F49, 2, 9) (dual of [(5764821, 2), 11529606, 10]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4936, 5764821, F49, 3, 9) (dual of [(5764821, 3), 17294427, 10]-NRT-code) [i]
3Digital (27, 36, 5764821)-net over F49 [i]
4Linear OOA(4936, 2882410, F49, 2, 9) (dual of [(2882410, 2), 5764784, 10]-NRT-code) [i]OOA Folding
5Linear OOA(4936, 1921607, F49, 3, 9) (dual of [(1921607, 3), 5764785, 10]-NRT-code) [i]
6Linear OOA(4936, 1441205, F49, 9, 9) (dual of [(1441205, 9), 12970809, 10]-NRT-code) [i]OOA Folding and Stacking with Additional Row