Information on Result #1302255

Linear OA(790, 823577, F7, 14) (dual of [823577, 823487, 15]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(789, 823575, F7, 14) (dual of [823575, 823486, 15]-code), using
    • construction X applied to Ce(14) ⊂ Ce(9) [i] based on
      1. linear OA(785, 823543, F7, 15) (dual of [823543, 823458, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
      3. linear OA(74, 32, F7, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,7)), using
  2. linear OA(789, 823576, F7, 13) (dual of [823576, 823487, 14]-code), using Gilbert–VarÅ¡amov bound and bm = 789 > Vbs−1(k−1) = 442468 288632 161639 166543 598575 464477 845611 885138 518837 347802 399263 838071 [i]
  3. linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using

Mode: 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(790, 823577, F7, 2, 14) (dual of [(823577, 2), 1647064, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(790, 823577, F7, 3, 14) (dual of [(823577, 3), 2470641, 15]-NRT-code) [i]
3Digital (76, 90, 823577)-net over F7 [i]