Information on Result #1299721

Linear OA(433, 1048590, F4, 5) (dual of [1048590, 1048557, 6]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(432, 1048588, F4, 5) (dual of [1048588, 1048556, 6]-code), using
    • construction X4 applied to Ce(4) ⊂ Ce(2) [i] based on
      1. linear OA(431, 1048576, F4, 5) (dual of [1048576, 1048545, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
      2. linear OA(421, 1048576, F4, 3) (dual of [1048576, 1048555, 4]-code or 1048576-cap in PG(20,4)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
      3. linear OA(411, 12, F4, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,4)), using
      4. linear OA(41, 12, F4, 1) (dual of [12, 11, 2]-code), using
  2. linear OA(432, 1048589, F4, 4) (dual of [1048589, 1048557, 5]-code), using Gilbert–VarÅ¡amov bound and bm = 432 > Vbs−1(k−1) = 5 188314 997829 671339 [i]
  3. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), 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(433, 1048590, F4, 2, 5) (dual of [(1048590, 2), 2097147, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(433, 1048590, F4, 3, 5) (dual of [(1048590, 3), 3145737, 6]-NRT-code) [i]
3Digital (28, 33, 1048590)-net over F4 [i]
4Linear OOA(433, 524295, F4, 2, 5) (dual of [(524295, 2), 1048557, 6]-NRT-code) [i]OOA Folding