Information on Result #1300002

Linear OA(499, 1048615, F4, 13) (dual of [1048615, 1048516, 14]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(496, 1048611, F4, 13) (dual of [1048611, 1048515, 14]-code), using
    • construction X applied to Ce(12) ⊂ Ce(8) [i] based on
      1. linear OA(491, 1048576, F4, 13) (dual of [1048576, 1048485, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
      2. linear OA(461, 1048576, F4, 9) (dual of [1048576, 1048515, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(45, 35, F4, 3) (dual of [35, 30, 4]-code or 35-cap in PG(4,4)), using
  2. linear OA(496, 1048612, F4, 10) (dual of [1048612, 1048516, 11]-code), using Gilbert–VarÅ¡amov bound and bm = 496 > Vbs−1(k−1) = 83146 557870 190371 295746 645348 412294 021664 619277 970008 [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

None.