Information on Result #678775

Linear OA(4217, 65600, F4, 34) (dual of [65600, 65383, 35]-code), using construction X applied to Ce(33) ⊂ Ce(25) based on
  1. linear OA(4201, 65536, F4, 34) (dual of [65536, 65335, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
  2. linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
  3. linear OA(416, 64, F4, 7) (dual of [64, 48, 8]-code), using
    • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]

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(4218, 65601, F4, 34) (dual of [65601, 65383, 35]-code) [i]Code Embedding in Larger Space
2Linear OA(4219, 65602, F4, 34) (dual of [65602, 65383, 35]-code) [i]
3Linear OOA(4217, 49367, F4, 2, 34) (dual of [(49367, 2), 98517, 35]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(4217, 49367, F4, 3, 34) (dual of [(49367, 3), 147884, 35]-NRT-code) [i]
5Digital (183, 217, 49367)-net over F4 [i]
6Linear OA(4219, 65603, F4, 34) (dual of [65603, 65384, 35]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OOA(4217, 32800, F4, 2, 34) (dual of [(32800, 2), 65383, 35]-NRT-code) [i]OOA Folding
8Linear OOA(4217, 21866, F4, 3, 34) (dual of [(21866, 3), 65381, 35]-NRT-code) [i]