Information on Result #684575

Linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code), using construction X applied to Ce(11) ⊂ Ce(7) based on
  1. linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  2. linear OA(743, 823543, F7, 8) (dual of [823543, 823500, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), 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(776, 823576, F7, 12) (dual of [823576, 823500, 13]-code) [i]Code Embedding in Larger Space
2Linear OA(777, 823577, F7, 12) (dual of [823577, 823500, 13]-code) [i]
3Linear OOA(775, 823575, F7, 2, 12) (dual of [(823575, 2), 1647075, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(775, 823575, F7, 3, 12) (dual of [(823575, 3), 2470650, 13]-NRT-code) [i]
5Digital (63, 75, 823575)-net over F7 [i]
6Linear OA(776, 823577, F7, 12) (dual of [823577, 823501, 13]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(777, 823579, F7, 12) (dual of [823579, 823502, 13]-code) [i]
8Linear OOA(775, 411787, F7, 2, 12) (dual of [(411787, 2), 823499, 13]-NRT-code) [i]OOA Folding
9Linear OOA(775, 274525, F7, 3, 12) (dual of [(274525, 3), 823500, 13]-NRT-code) [i]
10Linear OOA(775, 137262, F7, 12, 12) (dual of [(137262, 12), 1647069, 13]-NRT-code) [i]OA Folding and Stacking