Information on Result #699143

Linear OA(8156, 531473, F81, 17) (dual of [531473, 531417, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,4]) based on
  1. linear OA(8149, 531442, F81, 17) (dual of [531442, 531393, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(8125, 531442, F81, 9) (dual of [531442, 531417, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
  3. linear OA(817, 31, F81, 7) (dual of [31, 24, 8]-code or 31-arc in PG(6,81)), 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(8156, 531473, F81, 2, 17) (dual of [(531473, 2), 1062890, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8156, 531473, F81, 3, 17) (dual of [(531473, 3), 1594363, 18]-NRT-code) [i]
3Linear OOA(8156, 531473, F81, 4, 17) (dual of [(531473, 4), 2125836, 18]-NRT-code) [i]
4Digital (39, 56, 531473)-net over F81 [i]
5Linear OOA(8156, 265736, F81, 2, 17) (dual of [(265736, 2), 531416, 18]-NRT-code) [i]OOA Folding
6Linear OOA(8156, 177157, F81, 3, 17) (dual of [(177157, 3), 531415, 18]-NRT-code) [i]
7Linear OOA(8156, 132868, F81, 4, 17) (dual of [(132868, 4), 531416, 18]-NRT-code) [i]
8Linear OOA(8156, 66434, F81, 17, 17) (dual of [(66434, 17), 1129322, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row