Information on Result #678410

Linear OA(447, 262164, F4, 7) (dual of [262164, 262117, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
  1. linear OA(446, 262144, F4, 7) (dual of [262144, 262098, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. linear OA(428, 262144, F4, 5) (dual of [262144, 262116, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  3. linear OA(419, 20, F4, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,4)), using
  4. linear OA(41, 20, F4, 1) (dual of [20, 19, 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(448, 262165, F4, 7) (dual of [262165, 262117, 8]-code) [i]Code Embedding in Larger Space
2Linear OA(449, 262166, F4, 7) (dual of [262166, 262117, 8]-code) [i]
3Linear OOA(447, 262164, F4, 2, 7) (dual of [(262164, 2), 524281, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(447, 262164, F4, 3, 7) (dual of [(262164, 3), 786445, 8]-NRT-code) [i]
5Digital (40, 47, 262164)-net over F4 [i]
6Linear OA(448, 262166, F4, 7) (dual of [262166, 262118, 8]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(449, 262168, F4, 7) (dual of [262168, 262119, 8]-code) [i]
8Linear OOA(447, 131082, F4, 2, 7) (dual of [(131082, 2), 262117, 8]-NRT-code) [i]OOA Folding
9Linear OOA(447, 87388, F4, 3, 7) (dual of [(87388, 3), 262117, 8]-NRT-code) [i]