Information on Result #678016

Linear OA(4231, 4194368, F4, 27) (dual of [4194368, 4194137, 28]-code), using construction X applied to Ce(26) ⊂ Ce(20) based on
  1. linear OA(4221, 4194304, F4, 27) (dual of [4194304, 4194083, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
  3. linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
    • an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(4236, 4194375, F4, 27) (dual of [4194375, 4194139, 28]-code) [i]Construction X with VarÅ¡amov Bound
2Linear OA(4237, 4194377, F4, 27) (dual of [4194377, 4194140, 28]-code) [i]
3Linear OOA(4231, 2097184, F4, 2, 27) (dual of [(2097184, 2), 4194137, 28]-NRT-code) [i]OOA Folding
4Linear OOA(4231, 1398122, F4, 3, 27) (dual of [(1398122, 3), 4194135, 28]-NRT-code) [i]
5Linear OOA(4231, 322643, F4, 27, 27) (dual of [(322643, 27), 8711130, 28]-NRT-code) [i]OOA Folding and Stacking with Additional Row