Information on Result #699220

Linear OA(8124, 531452, F81, 8) (dual of [531452, 531428, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
  1. linear OA(8122, 531441, F81, 8) (dual of [531441, 531419, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(812, 11, F81, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,81)), 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 OA(948, 1062904, F9, 8) (dual of [1062904, 1062856, 9]-code) [i]Trace Code
2Linear OOA(8124, 531452, F81, 2, 8) (dual of [(531452, 2), 1062880, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(8124, 531452, F81, 3, 8) (dual of [(531452, 3), 1594332, 9]-NRT-code) [i]
4Linear OOA(8124, 531452, F81, 4, 8) (dual of [(531452, 4), 2125784, 9]-NRT-code) [i]
5Digital (16, 24, 531452)-net over F81 [i]
6Linear OOA(8124, 265726, F81, 2, 8) (dual of [(265726, 2), 531428, 9]-NRT-code) [i]OOA Folding
7Linear OOA(8124, 177150, F81, 3, 8) (dual of [(177150, 3), 531426, 9]-NRT-code) [i]
8Linear OOA(8124, 132863, F81, 4, 8) (dual of [(132863, 4), 531428, 9]-NRT-code) [i]
9Linear OOA(8124, 132863, F81, 8, 8) (dual of [(132863, 8), 1062880, 9]-NRT-code) [i]OA Folding and Stacking