Information on Result #699141

Linear OA(8168, 531473, F81, 21) (dual of [531473, 531405, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
  1. linear OA(8161, 531442, F81, 21) (dual of [531442, 531381, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(8137, 531442, F81, 13) (dual of [531442, 531405, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(8168, 531473, F81, 2, 21) (dual of [(531473, 2), 1062878, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8168, 531473, F81, 3, 21) (dual of [(531473, 3), 1594351, 22]-NRT-code) [i]
3Linear OOA(8168, 531473, F81, 4, 21) (dual of [(531473, 4), 2125824, 22]-NRT-code) [i]
4Digital (47, 68, 531473)-net over F81 [i]
5Linear OOA(8168, 265736, F81, 2, 21) (dual of [(265736, 2), 531404, 22]-NRT-code) [i]OOA Folding
6Linear OOA(8168, 177157, F81, 3, 21) (dual of [(177157, 3), 531403, 22]-NRT-code) [i]
7Linear OOA(8168, 132868, F81, 4, 21) (dual of [(132868, 4), 531404, 22]-NRT-code) [i]
8Linear OOA(8168, 53147, F81, 21, 21) (dual of [(53147, 21), 1116019, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row