Information on Result #731872

Linear OA(781, 5764862, F7, 11) (dual of [5764862, 5764781, 12]-code), using (u, u+v)-construction based on
  1. linear OA(77, 43, F7, 5) (dual of [43, 36, 6]-code), using
  2. linear OA(774, 5764819, F7, 11) (dual of [5764819, 5764745, 12]-code), using
    • construction X4 applied to Ce(10) ⊂ Ce(8) [i] based on
      1. linear OA(773, 5764801, F7, 11) (dual of [5764801, 5764728, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(757, 5764801, F7, 9) (dual of [5764801, 5764744, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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 OOA(781, 5764862, F7, 2, 11) (dual of [(5764862, 2), 11529643, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(781, 5764862, F7, 3, 11) (dual of [(5764862, 3), 17294505, 12]-NRT-code) [i]
3Digital (70, 81, 5764862)-net over F7 [i]
4Linear OOA(781, 2882431, F7, 2, 11) (dual of [(2882431, 2), 5764781, 12]-NRT-code) [i]OOA Folding
5Linear OOA(781, 1921620, F7, 3, 11) (dual of [(1921620, 3), 5764779, 12]-NRT-code) [i]
6Linear OOA(781, 1152972, F7, 11, 11) (dual of [(1152972, 11), 12682611, 12]-NRT-code) [i]OOA Folding and Stacking with Additional Row