Information on Result #672249

Linear OA(2196, 2097184, F2, 19) (dual of [2097184, 2096988, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2190, 2097152, F2, 19) (dual of [2097152, 2096962, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(2195, 2097183, F2, 18) (dual of [2097183, 2096988, 19]-code) [i]Truncation
2Linear OOA(2196, 1048592, F2, 2, 19) (dual of [(1048592, 2), 2096988, 20]-NRT-code) [i]OOA Folding
3Linear OOA(2196, 699061, F2, 3, 19) (dual of [(699061, 3), 2096987, 20]-NRT-code) [i]
4Linear OOA(2196, 524296, F2, 4, 19) (dual of [(524296, 4), 2096988, 20]-NRT-code) [i]
5Linear OOA(2196, 349530, F2, 6, 19) (dual of [(349530, 6), 2096984, 20]-NRT-code) [i]
6Linear OOA(2196, 262148, F2, 8, 19) (dual of [(262148, 8), 2096988, 20]-NRT-code) [i]
7Linear OOA(2196, 233020, F2, 19, 19) (dual of [(233020, 19), 4427184, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row