Information on Result #1299874

Linear OA(463, 1048600, F4, 8) (dual of [1048600, 1048537, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(462, 1048598, F4, 8) (dual of [1048598, 1048536, 9]-code), using
    • construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
      1. 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]
      2. linear OA(441, 1048576, F4, 6) (dual of [1048576, 1048535, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(421, 22, F4, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,4)), using
      4. linear OA(41, 22, F4, 1) (dual of [22, 21, 2]-code), using
  2. linear OA(462, 1048599, F4, 7) (dual of [1048599, 1048537, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 462 > Vbs−1(k−1) = 1 345996 089003 884842 401106 373357 163064 [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(463, 1048600, F4, 2, 8) (dual of [(1048600, 2), 2097137, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(463, 1048600, F4, 3, 8) (dual of [(1048600, 3), 3145737, 9]-NRT-code) [i]
3Digital (55, 63, 1048600)-net over F4 [i]
4Linear OOA(463, 524300, F4, 2, 8) (dual of [(524300, 2), 1048537, 9]-NRT-code) [i]OOA Folding