Information on Result #677968

Linear OA(4237, 4194342, F4, 29) (dual of [4194342, 4194105, 30]-code), using construction X applied to Ce(28) ⊂ Ce(24) based on
  1. linear OA(4232, 4194304, F4, 29) (dual of [4194304, 4194072, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  2. linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), 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(4237, 4194342, F4, 28) (dual of [4194342, 4194105, 29]-code) [i]Strength Reduction
2Linear OA(4238, 4194343, F4, 29) (dual of [4194343, 4194105, 30]-code) [i]Code Embedding in Larger Space
3Linear OA(4239, 4194344, F4, 29) (dual of [4194344, 4194105, 30]-code) [i]
4Linear OA(4240, 4194345, F4, 29) (dual of [4194345, 4194105, 30]-code) [i]
5Linear OA(4241, 4194346, F4, 29) (dual of [4194346, 4194105, 30]-code) [i]
6Linear OA(4236, 4194341, F4, 28) (dual of [4194341, 4194105, 29]-code) [i]Truncation
7Linear OOA(4237, 2097171, F4, 2, 29) (dual of [(2097171, 2), 4194105, 30]-NRT-code) [i]OOA Folding
8Linear OOA(4237, 1398114, F4, 3, 29) (dual of [(1398114, 3), 4194105, 30]-NRT-code) [i]
9Linear OOA(4237, 299595, F4, 29, 29) (dual of [(299595, 29), 8688018, 30]-NRT-code) [i]OOA Folding and Stacking with Additional Row