Information on Result #1300231

Linear OA(4142, 4194348, F4, 17) (dual of [4194348, 4194206, 18]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4138, 4194342, F4, 17) (dual of [4194342, 4194204, 18]-code), using
    • construction X applied to Ce(16) ⊂ Ce(12) [i] based on
      1. linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      2. linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      3. linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
  2. linear OA(4138, 4194344, F4, 14) (dual of [4194344, 4194206, 15]-code), using Gilbert–VarÅ¡amov bound and bm = 4138 > Vbs−1(k−1) = 31836 082663 839157 760061 847305 224581 307929 573661 375973 337093 381971 345910 294933 755928 [i]
  3. linear OA(42, 4, F4, 2) (dual of [4, 2, 3]-code or 4-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

None.