Information on Result #672196

Linear OA(2249, 4194336, F2, 23) (dual of [4194336, 4194087, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
  1. linear OA(2243, 4194304, F2, 23) (dual of [4194304, 4194061, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2248, 4194335, F2, 22) (dual of [4194335, 4194087, 23]-code) [i]Truncation
2Linear OOA(2249, 2097168, F2, 2, 23) (dual of [(2097168, 2), 4194087, 24]-NRT-code) [i]OOA Folding
3Linear OOA(2249, 1398112, F2, 3, 23) (dual of [(1398112, 3), 4194087, 24]-NRT-code) [i]
4Linear OOA(2249, 1048584, F2, 4, 23) (dual of [(1048584, 4), 4194087, 24]-NRT-code) [i]
5Linear OOA(2249, 838867, F2, 5, 23) (dual of [(838867, 5), 4194086, 24]-NRT-code) [i]
6Linear OOA(2249, 699056, F2, 6, 23) (dual of [(699056, 6), 4194087, 24]-NRT-code) [i]
7Linear OOA(2249, 524292, F2, 8, 23) (dual of [(524292, 8), 4194087, 24]-NRT-code) [i]
8Linear OOA(2249, 381303, F2, 23, 23) (dual of [(381303, 23), 8769720, 24]-NRT-code) [i]OOA Folding and Stacking with Additional Row