Information on Result #1300471

Linear OA(4175, 4194347, F4, 21) (dual of [4194347, 4194172, 22]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4171, 4194342, F4, 21) (dual of [4194342, 4194171, 22]-code), using
    • construction X applied to Ce(20) ⊂ Ce(16) [i] based on
      1. linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
      2. 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]
      3. linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
  2. linear OA(4171, 4194343, F4, 17) (dual of [4194343, 4194172, 18]-code), using Gilbert–VarÅ¡amov bound and bm = 4171 > Vbs−1(k−1) = 18876 872258 000920 690441 124173 443944 779398 066834 064527 186036 300300 968997 444408 903956 027719 166923 234126 [i]
  3. linear OA(43, 4, F4, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,4) or 4-cap in PG(2,4)), 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.