Information on Result #672182

Linear OA(2156, 4194328, F2, 15) (dual of [4194328, 4194172, 16]-code), using construction X4 applied to Ce(14) ⊂ Ce(12) based on
  1. linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(2133, 4194304, F2, 13) (dual of [4194304, 4194171, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  3. linear OA(223, 24, F2, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,2)), using
  4. linear OA(21, 24, F2, 1) (dual of [24, 23, 2]-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(2156, 4194328, F2, 14) (dual of [4194328, 4194172, 15]-code) [i]Strength Reduction
2Linear OA(2157, 4194329, F2, 15) (dual of [4194329, 4194172, 16]-code) [i]Code Embedding in Larger Space
3Linear OA(2158, 4194330, F2, 15) (dual of [4194330, 4194172, 16]-code) [i]
4Linear OA(2159, 4194331, F2, 15) (dual of [4194331, 4194172, 16]-code) [i]
5Linear OA(2160, 4194332, F2, 15) (dual of [4194332, 4194172, 16]-code) [i]
6Linear OA(2155, 4194327, F2, 14) (dual of [4194327, 4194172, 15]-code) [i]Truncation
7Linear OOA(2156, 2097164, F2, 2, 15) (dual of [(2097164, 2), 4194172, 16]-NRT-code) [i]OOA Folding
8Linear OOA(2156, 1048582, F2, 4, 15) (dual of [(1048582, 4), 4194172, 16]-NRT-code) [i]