Information on Result #684559

Linear OA(7109, 823567, F7, 18) (dual of [823567, 823458, 19]-code), using construction X applied to Ce(17) ⊂ Ce(14) based on
  1. linear OA(7106, 823543, F7, 18) (dual of [823543, 823437, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(73, 24, F7, 2) (dual of [24, 21, 3]-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(7110, 823568, F7, 18) (dual of [823568, 823458, 19]-code) [i]Code Embedding in Larger Space
2Linear OOA(7109, 573841, F7, 2, 18) (dual of [(573841, 2), 1147573, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(7109, 573841, F7, 3, 18) (dual of [(573841, 3), 1721414, 19]-NRT-code) [i]
4Digital (91, 109, 573841)-net over F7 [i]
5Linear OOA(7109, 411783, F7, 2, 18) (dual of [(411783, 2), 823457, 19]-NRT-code) [i]OOA Folding
6Linear OOA(7109, 274522, F7, 3, 18) (dual of [(274522, 3), 823457, 19]-NRT-code) [i]
7Linear OOA(7109, 91507, F7, 18, 18) (dual of [(91507, 18), 1647017, 19]-NRT-code) [i]OA Folding and Stacking