Information on Result #684675

Linear OA(7109, 117685, F7, 20) (dual of [117685, 117576, 21]-code), using construction X applied to Ce(19) ⊂ Ce(14) based on
  1. linear OA(7103, 117649, F7, 20) (dual of [117649, 117546, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(76, 36, F7, 4) (dual of [36, 30, 5]-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, 117686, F7, 20) (dual of [117686, 117576, 21]-code) [i]Code Embedding in Larger Space
2Linear OOA(7109, 117685, F7, 2, 20) (dual of [(117685, 2), 235261, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(7109, 117685, F7, 3, 20) (dual of [(117685, 3), 352946, 21]-NRT-code) [i]
4Digital (89, 109, 117685)-net over F7 [i]
5Linear OA(7110, 117687, F7, 20) (dual of [117687, 117577, 21]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(7109, 58842, F7, 2, 20) (dual of [(58842, 2), 117575, 21]-NRT-code) [i]OOA Folding
7Linear OOA(7109, 39228, F7, 3, 20) (dual of [(39228, 3), 117575, 21]-NRT-code) [i]
8Linear OOA(7109, 11768, F7, 20, 20) (dual of [(11768, 20), 235251, 21]-NRT-code) [i]OA Folding and Stacking