Information on Result #678184

Linear OA(452, 1048598, F4, 7) (dual of [1048598, 1048546, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) 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

Mode: Constructive and 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 OA(453, 1048599, F4, 7) (dual of [1048599, 1048546, 8]-code) [i]Code Embedding in Larger Space
2Linear OA(454, 1048600, F4, 7) (dual of [1048600, 1048546, 8]-code) [i]
3Linear OA(455, 1048604, F4, 7) (dual of [1048604, 1048549, 8]-code) [i](u, u+v)-Construction
4Linear OOA(452, 1048598, F4, 2, 7) (dual of [(1048598, 2), 2097144, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(452, 1048598, F4, 3, 7) (dual of [(1048598, 3), 3145742, 8]-NRT-code) [i]
6Digital (45, 52, 1048598)-net over F4 [i]
7Linear OA(453, 1048600, F4, 7) (dual of [1048600, 1048547, 8]-code) [i]Construction X with VarÅ¡amov Bound
8Linear OA(454, 1048602, F4, 7) (dual of [1048602, 1048548, 8]-code) [i]
9Linear OOA(452, 524299, F4, 2, 7) (dual of [(524299, 2), 1048546, 8]-NRT-code) [i]OOA Folding