Information on Result #699538

Linear OA(8136, 6578, F81, 16) (dual of [6578, 6542, 17]-code), using construction X applied to Ce(15) ⊂ Ce(9) based on
  1. linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(8119, 6561, F81, 10) (dual of [6561, 6542, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(815, 17, F81, 5) (dual of [17, 12, 6]-code or 17-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(8136, 4456, F81, 2, 16) (dual of [(4456, 2), 8876, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(8136, 4456, F81, 3, 16) (dual of [(4456, 3), 13332, 17]-NRT-code) [i]
3Linear OOA(8136, 4456, F81, 4, 16) (dual of [(4456, 4), 17788, 17]-NRT-code) [i]
4Digital (20, 36, 4456)-net over F81 [i]
5Linear OOA(8136, 3289, F81, 2, 16) (dual of [(3289, 2), 6542, 17]-NRT-code) [i]OOA Folding
6Linear OOA(8136, 2192, F81, 3, 16) (dual of [(2192, 3), 6540, 17]-NRT-code) [i]
7Linear OOA(8136, 1644, F81, 4, 16) (dual of [(1644, 4), 6540, 17]-NRT-code) [i]
8Linear OOA(8136, 822, F81, 16, 16) (dual of [(822, 16), 13116, 17]-NRT-code) [i]OA Folding and Stacking