Information on Result #1302076

Linear OA(756, 16833, F7, 12) (dual of [16833, 16777, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(755, 16831, F7, 12) (dual of [16831, 16776, 13]-code), using
    • construction X applied to Ce(11) ⊂ Ce(7) [i] based on
      1. linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
      2. linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), using
  2. linear OA(755, 16832, F7, 11) (dual of [16832, 16777, 12]-code), using Gilbert–VarÅ¡amov bound and bm = 755 > Vbs−1(k−1) = 30 320079 540736 878444 288575 074557 682732 239799 [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(756, 16833, F7, 2, 12) (dual of [(16833, 2), 33610, 13]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(756, 16833, F7, 3, 12) (dual of [(16833, 3), 50443, 13]-NRT-code) [i]
3Digital (44, 56, 16833)-net over F7 [i]