Information on Result #1299768

Linear OA(444, 65558, F4, 7) (dual of [65558, 65514, 8]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(442, 65554, F4, 7) (dual of [65554, 65512, 8]-code), using
    • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
      1. linear OA(441, 65536, F4, 7) (dual of [65536, 65495, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. linear OA(425, 65536, F4, 5) (dual of [65536, 65511, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(442, 65556, F4, 6) (dual of [65556, 65514, 7]-code), using Gilbert–VarÅ¡amov bound and bm = 442 > Vbs−1(k−1) = 2 451313 900934 462172 681304 [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(444, 65558, F4, 2, 7) (dual of [(65558, 2), 131072, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(444, 65558, F4, 3, 7) (dual of [(65558, 3), 196630, 8]-NRT-code) [i]
3Digital (37, 44, 65558)-net over F4 [i]
4Linear OOA(444, 32779, F4, 2, 7) (dual of [(32779, 2), 65514, 8]-NRT-code) [i]OOA Folding