Information on Result #678683

Linear OA(442, 65554, F4, 7) (dual of [65554, 65512, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) 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

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(443, 65555, F4, 7) (dual of [65555, 65512, 8]-code) [i]Code Embedding in Larger Space
2Linear OA(444, 65556, F4, 7) (dual of [65556, 65512, 8]-code) [i]
3Linear OOA(442, 65554, F4, 2, 7) (dual of [(65554, 2), 131066, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(442, 65554, F4, 3, 7) (dual of [(65554, 3), 196620, 8]-NRT-code) [i]
5Digital (35, 42, 65554)-net over F4 [i]
6Linear OA(443, 65556, F4, 7) (dual of [65556, 65513, 8]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(444, 65558, F4, 7) (dual of [65558, 65514, 8]-code) [i]
8Linear OOA(442, 32777, F4, 2, 7) (dual of [(32777, 2), 65512, 8]-NRT-code) [i]OOA Folding
9Linear OOA(442, 21851, F4, 7, 7) (dual of [(21851, 7), 152915, 8]-NRT-code) [i]OOA Folding and Stacking with Additional Row