Information on Result #679664

Linear OA(432, 4110, F4, 7) (dual of [4110, 4078, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
  1. linear OA(431, 4096, F4, 7) (dual of [4096, 4065, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(419, 4096, F4, 5) (dual of [4096, 4077, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(413, 14, F4, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,4)), using
  4. linear OA(41, 14, F4, 1) (dual of [14, 13, 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(433, 4111, F4, 7) (dual of [4111, 4078, 8]-code) [i]Code Embedding in Larger Space
2Linear OA(434, 4112, F4, 7) (dual of [4112, 4078, 8]-code) [i]
3Linear OOA(432, 4110, F4, 2, 7) (dual of [(4110, 2), 8188, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(432, 4110, F4, 3, 7) (dual of [(4110, 3), 12298, 8]-NRT-code) [i]
5Digital (25, 32, 4110)-net over F4 [i]
6Linear OA(433, 4118, F4, 7) (dual of [4118, 4085, 8]-code) [i]VarÅ¡amov–Edel Lengthening
7Linear OA(434, 4149, F4, 7) (dual of [4149, 4115, 8]-code) [i]
8Linear OA(433, 4112, F4, 7) (dual of [4112, 4079, 8]-code) [i]Construction X with VarÅ¡amov Bound
9Linear OA(434, 4114, F4, 7) (dual of [4114, 4080, 8]-code) [i]
10Linear OOA(432, 2055, F4, 2, 7) (dual of [(2055, 2), 4078, 8]-NRT-code) [i]OOA Folding
11Linear OOA(432, 1370, F4, 3, 7) (dual of [(1370, 3), 4078, 8]-NRT-code) [i]