Information on Result #1299802

Linear OA(453, 83, F4, 25) (dual of [83, 30, 26]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(448, 75, F4, 25) (dual of [75, 27, 26]-code), using
    • construction XX applied to C([1,77]) ⊂ C([1,65]) ⊂ C([1,62]) [i] based on
      1. linear OA(443, 63, F4, 25) (dual of [63, 20, 26]-code), using contraction [i] based on linear OA(4169, 189, F4, 77) (dual of [189, 20, 78]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,77], and designed minimum distance d ≥ |I|+1 = 78 [i]
      2. linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [i]
      3. linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
      4. linear OA(44, 11, F4, 3) (dual of [11, 7, 4]-code or 11-cap in PG(3,4)), using
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
  2. linear OA(448, 78, F4, 22) (dual of [78, 30, 23]-code), using Gilbert–VarÅ¡amov bound and bm = 448 > Vbs−1(k−1) = 47601 737119 917451 127664 056896 [i]
  3. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

None.