Information on Result #699133

Linear OA(8172, 531465, F81, 23) (dual of [531465, 531393, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,8]) based on
  1. linear OA(8167, 531442, F81, 23) (dual of [531442, 531375, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442 | 816−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
  2. 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]
  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(8172, 307529, F81, 2, 23) (dual of [(307529, 2), 614986, 24]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8172, 307529, F81, 3, 23) (dual of [(307529, 3), 922515, 24]-NRT-code) [i]
3Linear OOA(8172, 307529, F81, 4, 23) (dual of [(307529, 4), 1230044, 24]-NRT-code) [i]
4Digital (49, 72, 307529)-net over F81 [i]
5Linear OOA(8172, 265732, F81, 2, 23) (dual of [(265732, 2), 531392, 24]-NRT-code) [i]OOA Folding
6Linear OOA(8172, 177155, F81, 3, 23) (dual of [(177155, 3), 531393, 24]-NRT-code) [i]
7Linear OOA(8172, 132866, F81, 4, 23) (dual of [(132866, 4), 531392, 24]-NRT-code) [i]