Information on Result #677980

Linear OA(4105, 4194342, F4, 13) (dual of [4194342, 4194237, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
  1. linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(467, 4194304, F4, 9) (dual of [4194304, 4194237, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(4105, 4194342, F4, 12) (dual of [4194342, 4194237, 13]-code) [i]Strength Reduction
2Linear OA(4106, 4194343, F4, 13) (dual of [4194343, 4194237, 14]-code) [i]Code Embedding in Larger Space
3Linear OA(4107, 4194344, F4, 13) (dual of [4194344, 4194237, 14]-code) [i]
4Linear OA(4108, 4194345, F4, 13) (dual of [4194345, 4194237, 14]-code) [i]
5Linear OA(4104, 4194341, F4, 12) (dual of [4194341, 4194237, 13]-code) [i]Truncation
6Linear OOA(4105, 2097171, F4, 2, 13) (dual of [(2097171, 2), 4194237, 14]-NRT-code) [i]OOA Folding
7Linear OOA(4105, 1398114, F4, 3, 13) (dual of [(1398114, 3), 4194237, 14]-NRT-code) [i]
8Linear OOA(4105, 699056, F4, 13, 13) (dual of [(699056, 13), 9087623, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row