Information on Result #684463

Linear OA(798, 5764819, F7, 14) (dual of [5764819, 5764721, 15]-code), using construction X4 applied to Ce(14) ⊂ Ce(11) based on
  1. linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(781, 5764801, F7, 12) (dual of [5764801, 5764720, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(717, 18, F7, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,7)), using
  4. linear OA(71, 18, F7, 1) (dual of [18, 17, 2]-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, 5764820, F7, 14) (dual of [5764820, 5764721, 15]-code) [i]Code Embedding in Larger Space
2Linear OOA(798, 5764819, F7, 2, 14) (dual of [(5764819, 2), 11529540, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(798, 5764819, F7, 3, 14) (dual of [(5764819, 3), 17294359, 15]-NRT-code) [i]
4Digital (84, 98, 5764819)-net over F7 [i]
5Linear OA(799, 5764821, F7, 14) (dual of [5764821, 5764722, 15]-code) [i]Construction X with VarÅ¡amov Bound