Information on Result #1302147

Linear OA(769, 16841, F7, 15) (dual of [16841, 16772, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(768, 16839, F7, 15) (dual of [16839, 16771, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(8) [i] based on
      1. linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
      2. linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(77, 32, F7, 5) (dual of [32, 25, 6]-code), using
  2. linear OA(768, 16840, F7, 14) (dual of [16840, 16772, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 768 > Vbs−1(k−1) = 18 274332 684976 819635 107453 068386 991466 558295 990329 181943 [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(769, 16841, F7, 2, 15) (dual of [(16841, 2), 33613, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(769, 16841, F7, 3, 15) (dual of [(16841, 3), 50454, 16]-NRT-code) [i]
3Digital (54, 69, 16841)-net over F7 [i]