Information on Result #699132

Linear OA(8178, 531465, F81, 25) (dual of [531465, 531387, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,9]) based on
  1. linear OA(8173, 531442, F81, 25) (dual of [531442, 531369, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
  2. linear OA(8155, 531442, F81, 19) (dual of [531442, 531387, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
  3. linear OA(815, 23, F81, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,81)), 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(8178, 288819, F81, 2, 25) (dual of [(288819, 2), 577560, 26]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8178, 288819, F81, 3, 25) (dual of [(288819, 3), 866379, 26]-NRT-code) [i]
3Linear OOA(8178, 288819, F81, 4, 25) (dual of [(288819, 4), 1155198, 26]-NRT-code) [i]
4Digital (53, 78, 288819)-net over F81 [i]
5Linear OOA(8178, 265732, F81, 2, 25) (dual of [(265732, 2), 531386, 26]-NRT-code) [i]OOA Folding
6Linear OOA(8178, 177155, F81, 3, 25) (dual of [(177155, 3), 531387, 26]-NRT-code) [i]
7Linear OOA(8178, 132866, F81, 4, 25) (dual of [(132866, 4), 531386, 26]-NRT-code) [i]