Information on Result #1299446

Linear OA(3219, 6620, F3, 38) (dual of [6620, 6401, 39]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(3215, 6614, F3, 38) (dual of [6614, 6399, 39]-code), using
    • construction X applied to Ce(37) ⊂ Ce(30) [i] based on
      1. linear OA(3201, 6561, F3, 38) (dual of [6561, 6360, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
      2. linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
      3. linear OA(314, 53, F3, 6) (dual of [53, 39, 7]-code), using
  2. linear OA(3215, 6616, F3, 35) (dual of [6616, 6401, 36]-code), using Gilbert–VarÅ¡amov bound and bm = 3215 > Vbs−1(k−1) = 423740 040963 327081 376729 607038 960304 312488 540337 524895 756966 080835 476276 986795 578649 262613 456504 430923 [i]
  3. linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), 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(3219, 3310, F3, 2, 38) (dual of [(3310, 2), 6401, 39]-NRT-code) [i]OOA Folding