Information on Result #1298749

Linear OA(3158, 19734, F3, 24) (dual of [19734, 19576, 25]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3154, 19729, F3, 24) (dual of [19729, 19575, 25]-code), using
    • construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
      1. linear OA(3145, 19684, F3, 25) (dual of [19684, 19539, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
      2. linear OA(3109, 19684, F3, 19) (dual of [19684, 19575, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684 | 318−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
      3. linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
  2. linear OA(3154, 19730, F3, 20) (dual of [19730, 19576, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 3154 > Vbs−1(k−1) = 17294 803787 254711 825485 861687 539159 626822 775799 118916 107242 578695 270851 [i]
  3. linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), 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(3158, 9867, F3, 2, 24) (dual of [(9867, 2), 19576, 25]-NRT-code) [i]OOA Folding
2Linear OOA(3158, 6578, F3, 3, 24) (dual of [(6578, 3), 19576, 25]-NRT-code) [i]