Information on Result #1300880

Linear OA(4221, 262203, F4, 31) (dual of [262203, 261982, 32]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4218, 262199, F4, 31) (dual of [262199, 261981, 32]-code), using
    • construction X applied to Ce(30) ⊂ Ce(24) [i] based on
      1. linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
      2. linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
      3. linear OA(410, 55, F4, 5) (dual of [55, 45, 6]-code), using
  2. linear OA(4218, 262200, F4, 28) (dual of [262200, 261982, 29]-code), using Gilbert–VarÅ¡amov bound and bm = 4218 > Vbs−1(k−1) = 140527 859902 852557 796891 155194 679017 636193 525455 261642 025250 800901 029061 384610 061358 858809 437171 460866 137647 383459 876956 967680 687408 [i]
  3. linear OA(42, 3, F4, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,4)), 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(4221, 87401, F4, 3, 31) (dual of [(87401, 3), 261982, 32]-NRT-code) [i]OOA Folding