Information on Result #1299818

Linear OA(451, 65556, F4, 8) (dual of [65556, 65505, 9]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(450, 65554, F4, 8) (dual of [65554, 65504, 9]-code), using
    • construction X4 applied to Ce(8) ⊂ Ce(5) [i] based on
      1. linear OA(449, 65536, F4, 9) (dual of [65536, 65487, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(433, 65536, F4, 6) (dual of [65536, 65503, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      3. linear OA(417, 18, F4, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,4)), using
      4. linear OA(41, 18, F4, 1) (dual of [18, 17, 2]-code), using
  2. linear OA(450, 65555, F4, 7) (dual of [65555, 65505, 8]-code), using Gilbert–VarÅ¡amov bound and bm = 450 > Vbs−1(k−1) = 80334 868316 187991 022541 334696 [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(451, 65556, F4, 2, 8) (dual of [(65556, 2), 131061, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(451, 65556, F4, 3, 8) (dual of [(65556, 3), 196617, 9]-NRT-code) [i]
3Digital (43, 51, 65556)-net over F4 [i]
4Linear OOA(451, 32778, F4, 2, 8) (dual of [(32778, 2), 65505, 9]-NRT-code) [i]OOA Folding