Information on Result #1324338

Linear OA(7107, 5764853, F7, 15) (dual of [5764853, 5764746, 16]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(7105, 5764849, F7, 15) (dual of [5764849, 5764744, 16]-code), using
    • construction X applied to Ce(14) ⊂ Ce(8) [i] 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(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(78, 48, F7, 5) (dual of [48, 40, 6]-code), using
  2. linear OA(7105, 5764851, F7, 14) (dual of [5764851, 5764746, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 7105 > Vbs−1(k−1) = 16290 123458 519376 510458 909445 034567 305068 064200 016689 979355 177477 750605 439027 902128 464561 [i]
  3. linear OA(70, 2, F7, 0) (dual of [2, 2, 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(7107, 5764853, F7, 2, 15) (dual of [(5764853, 2), 11529599, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(7107, 5764853, F7, 3, 15) (dual of [(5764853, 3), 17294452, 16]-NRT-code) [i]
3Digital (92, 107, 5764853)-net over F7 [i]