Information on Result #1324204

Linear OA(4243, 65627, F4, 37) (dual of [65627, 65384, 38]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4241, 65624, F4, 37) (dual of [65624, 65383, 38]-code), using
    • construction X applied to Ce(36) ⊂ Ce(25) [i] based on
      1. linear OA(4217, 65536, F4, 37) (dual of [65536, 65319, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
      2. linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
      3. linear OA(424, 88, F4, 10) (dual of [88, 64, 11]-code), using
  2. linear OA(4241, 65625, F4, 35) (dual of [65625, 65384, 36]-code), using Gilbert–VarÅ¡amov bound and bm = 4241 > Vbs−1(k−1) = 3376 381935 288313 800674 534347 103599 811112 648911 682478 925694 505556 189333 786571 998350 821227 900770 850197 222332 426988 499930 349557 614571 798864 379802 [i]
  3. linear OA(41, 2, F4, 1) (dual of [2, 1, 2]-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(4243, 65627, F4, 2, 37) (dual of [(65627, 2), 131011, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4243, 65627, F4, 3, 37) (dual of [(65627, 3), 196638, 38]-NRT-code) [i]
3Digital (206, 243, 65627)-net over F4 [i]