Information on Result #1299825

Linear OA(454, 1048602, F4, 7) (dual of [1048602, 1048548, 8]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(451, 1048576, F4, 7) (dual of [1048576, 1048525, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. 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]
      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(452, 1048600, F4, 6) (dual of [1048600, 1048548, 7]-code), using Gilbert–VarÅ¡amov bound and bm = 452 > Vbs−1(k−1) = 2 567253 604063 444960 004641 159678 [i]
  3. linear OA(40, 2, F4, 0) (dual of [2, 2, 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(454, 1048602, F4, 2, 7) (dual of [(1048602, 2), 2097150, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(454, 1048602, F4, 3, 7) (dual of [(1048602, 3), 3145752, 8]-NRT-code) [i]
3Digital (47, 54, 1048602)-net over F4 [i]
4Linear OOA(454, 524301, F4, 2, 7) (dual of [(524301, 2), 1048548, 8]-NRT-code) [i]OOA Folding