Information on Result #1300577

Linear OA(4184, 1048640, F4, 23) (dual of [1048640, 1048456, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4181, 1048636, F4, 23) (dual of [1048636, 1048455, 24]-code), using
    • construction X applied to Ce(22) ⊂ Ce(16) [i] based on
      1. linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
      2. linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
      3. linear OA(410, 60, F4, 5) (dual of [60, 50, 6]-code), using
  2. linear OA(4181, 1048637, F4, 20) (dual of [1048637, 1048456, 21]-code), using Gilbert–VarÅ¡amov bound and bm = 4181 > Vbs−1(k−1) = 23551 117540 645290 913343 140650 503927 701721 241101 204914 258870 588117 105675 919822 298915 120658 537361 265736 839379 [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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(4184, 524320, F4, 2, 23) (dual of [(524320, 2), 1048456, 24]-NRT-code) [i]OOA Folding