Information on Result #672987

Linear OA(2210, 2085, F2, 37) (dual of [2085, 1875, 38]-code), using construction XX applied to Ce(36) ⊂ Ce(32) ⊂ Ce(30) based on
  1. linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
  3. linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  4. linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
  5. linear OA(21, 5, F2, 1) (dual of [5, 4, 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(2209, 2084, F2, 36) (dual of [2084, 1875, 37]-code) [i]Truncation
2Linear OOA(2210, 1042, F2, 2, 37) (dual of [(1042, 2), 1874, 38]-NRT-code) [i]OOA Folding
3Linear OOA(2210, 695, F2, 3, 37) (dual of [(695, 3), 1875, 38]-NRT-code) [i]
4Linear OOA(2210, 521, F2, 4, 37) (dual of [(521, 4), 1874, 38]-NRT-code) [i]
5Linear OOA(2210, 417, F2, 5, 37) (dual of [(417, 5), 1875, 38]-NRT-code) [i]
6Linear OOA(2210, 347, F2, 6, 37) (dual of [(347, 6), 1872, 38]-NRT-code) [i]