Information on Result #672303

Linear OA(2187, 1048608, F2, 19) (dual of [1048608, 1048421, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(2141, 1048576, F2, 15) (dual of [1048576, 1048435, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, 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(2186, 1048607, F2, 18) (dual of [1048607, 1048421, 19]-code) [i]Truncation
2Linear OOA(2187, 524304, F2, 2, 19) (dual of [(524304, 2), 1048421, 20]-NRT-code) [i]OOA Folding
3Linear OOA(2187, 349536, F2, 3, 19) (dual of [(349536, 3), 1048421, 20]-NRT-code) [i]
4Linear OOA(2187, 262152, F2, 4, 19) (dual of [(262152, 4), 1048421, 20]-NRT-code) [i]
5Linear OOA(2187, 209721, F2, 5, 19) (dual of [(209721, 5), 1048418, 20]-NRT-code) [i]
6Linear OOA(2187, 174768, F2, 6, 19) (dual of [(174768, 6), 1048421, 20]-NRT-code) [i]
7Linear OOA(2187, 149801, F2, 7, 19) (dual of [(149801, 7), 1048420, 20]-NRT-code) [i]
8Linear OOA(2187, 131076, F2, 8, 19) (dual of [(131076, 8), 1048421, 20]-NRT-code) [i]