Information on Result #684677

Linear OA(798, 117686, F7, 18) (dual of [117686, 117588, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
  1. linear OA(791, 117649, F7, 18) (dual of [117649, 117558, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(761, 117649, F7, 12) (dual of [117649, 117588, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(77, 37, F7, 5) (dual of [37, 30, 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(799, 117687, F7, 18) (dual of [117687, 117588, 19]-code) [i]Code Embedding in Larger Space
2Linear OA(7100, 117688, F7, 18) (dual of [117688, 117588, 19]-code) [i]
3Linear OA(7101, 117689, F7, 18) (dual of [117689, 117588, 19]-code) [i]
4Linear OOA(798, 117686, F7, 2, 18) (dual of [(117686, 2), 235274, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(798, 117686, F7, 3, 18) (dual of [(117686, 3), 352960, 19]-NRT-code) [i]
6Digital (80, 98, 117686)-net over F7 [i]
7Linear OA(799, 117688, F7, 18) (dual of [117688, 117589, 19]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(7100, 117690, F7, 18) (dual of [117690, 117590, 19]-code) [i]
9Linear OOA(798, 58843, F7, 2, 18) (dual of [(58843, 2), 117588, 19]-NRT-code) [i]OOA Folding
10Linear OOA(798, 39228, F7, 3, 18) (dual of [(39228, 3), 117586, 19]-NRT-code) [i]
11Linear OOA(798, 13076, F7, 18, 18) (dual of [(13076, 18), 235270, 19]-NRT-code) [i]OA Folding and Stacking