Information on Result #1298640

Linear OA(3141, 59090, F3, 20) (dual of [59090, 58949, 21]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3137, 59085, F3, 20) (dual of [59085, 58948, 21]-code), using
    • construction X applied to Ce(19) ⊂ Ce(15) [i] based on
      1. linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
      2. linear OA(3101, 59049, F3, 16) (dual of [59049, 58948, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
      3. linear OA(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
  2. linear OA(3137, 59086, F3, 16) (dual of [59086, 58949, 17]-code), using Gilbert–VarÅ¡amov bound and bm = 3137 > Vbs−1(k−1) = 9340 975160 470543 527220 740992 574894 489043 808085 538300 105631 387859 [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(3141, 29545, F3, 2, 20) (dual of [(29545, 2), 58949, 21]-NRT-code) [i]OOA Folding