Information on Result #684834

Linear OA(773, 16839, F7, 16) (dual of [16839, 16766, 17]-code), using construction X applied to Ce(15) ⊂ Ce(9) based on
  1. linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  2. linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), 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(774, 16840, F7, 16) (dual of [16840, 16766, 17]-code) [i]Code Embedding in Larger Space
2Linear OA(775, 16841, F7, 16) (dual of [16841, 16766, 17]-code) [i]
3Linear OA(776, 16842, F7, 16) (dual of [16842, 16766, 17]-code) [i]
4Linear OOA(773, 16839, F7, 2, 16) (dual of [(16839, 2), 33605, 17]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(773, 16839, F7, 3, 16) (dual of [(16839, 3), 50444, 17]-NRT-code) [i]
6Digital (57, 73, 16839)-net over F7 [i]
7Linear OA(774, 16841, F7, 16) (dual of [16841, 16767, 17]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OOA(773, 8419, F7, 2, 16) (dual of [(8419, 2), 16765, 17]-NRT-code) [i]OOA Folding
9Linear OOA(773, 5613, F7, 3, 16) (dual of [(5613, 3), 16766, 17]-NRT-code) [i]