Information on Result #699230

Linear OA(8137, 531456, F81, 12) (dual of [531456, 531419, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) based on
  1. linear OA(8134, 531441, F81, 12) (dual of [531441, 531407, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. 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]
  3. linear OA(813, 15, F81, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,81) or 15-cap in PG(2,81)), 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(8137, 420173, F81, 2, 12) (dual of [(420173, 2), 840309, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8137, 420173, F81, 3, 12) (dual of [(420173, 3), 1260482, 13]-NRT-code) [i]
3Linear OOA(8137, 420173, F81, 4, 12) (dual of [(420173, 4), 1680655, 13]-NRT-code) [i]
4Digital (25, 37, 420173)-net over F81 [i]
5Linear OOA(8137, 265728, F81, 2, 12) (dual of [(265728, 2), 531419, 13]-NRT-code) [i]OOA Folding
6Linear OOA(8137, 177152, F81, 3, 12) (dual of [(177152, 3), 531419, 13]-NRT-code) [i]
7Linear OOA(8137, 132864, F81, 4, 12) (dual of [(132864, 4), 531419, 13]-NRT-code) [i]
8Linear OOA(8137, 88576, F81, 12, 12) (dual of [(88576, 12), 1062875, 13]-NRT-code) [i]OA Folding and Stacking