Information on Result #1297915

Linear OA(343, 59073, F3, 6) (dual of [59073, 59030, 7]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(342, 59071, F3, 6) (dual of [59071, 59029, 7]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(3) [i] based on
      1. linear OA(341, 59049, F3, 7) (dual of [59049, 59008, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(321, 59049, F3, 4) (dual of [59049, 59028, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(321, 22, F3, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,3)), using
      4. linear OA(31, 22, F3, 1) (dual of [22, 21, 2]-code), using
  2. linear OA(342, 59072, F3, 5) (dual of [59072, 59030, 6]-code), using Gilbert–VarÅ¡amov bound and bm = 342 > Vbs−1(k−1) = 8 116646 366233 929483 [i]
  3. linear OA(30, 1, F3, 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(343, 59073, F3, 2, 6) (dual of [(59073, 2), 118103, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(343, 59073, F3, 3, 6) (dual of [(59073, 3), 177176, 7]-NRT-code) [i]
3Linear OOA(343, 59073, F3, 4, 6) (dual of [(59073, 4), 236249, 7]-NRT-code) [i]
4Linear OOA(343, 59073, F3, 5, 6) (dual of [(59073, 5), 295322, 7]-NRT-code) [i]