Information on Result #678003

Linear OA(4152, 4194356, F4, 18) (dual of [4194356, 4194204, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
  1. linear OA(4144, 4194304, F4, 18) (dual of [4194304, 4194160, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. 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]
  3. linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-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(4153, 4194357, F4, 18) (dual of [4194357, 4194204, 19]-code) [i]Code Embedding in Larger Space
2Linear OA(4154, 4194358, F4, 18) (dual of [4194358, 4194204, 19]-code) [i]
3Linear OA(4155, 4194359, F4, 18) (dual of [4194359, 4194204, 19]-code) [i]
4Linear OA(4156, 4194360, F4, 18) (dual of [4194360, 4194204, 19]-code) [i]
5Linear OA(4155, 4194360, F4, 18) (dual of [4194360, 4194205, 19]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(4156, 4194362, F4, 18) (dual of [4194362, 4194206, 19]-code) [i]
7Linear OOA(4152, 2097178, F4, 2, 18) (dual of [(2097178, 2), 4194204, 19]-NRT-code) [i]OOA Folding
8Linear OOA(4152, 1398118, F4, 3, 18) (dual of [(1398118, 3), 4194202, 19]-NRT-code) [i]
9Linear OOA(4152, 466039, F4, 18, 18) (dual of [(466039, 18), 8388550, 19]-NRT-code) [i]OA Folding and Stacking