Information on Result #672543

Linear OA(2247, 65568, F2, 31) (dual of [65568, 65321, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
  1. linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(2246, 65567, F2, 30) (dual of [65567, 65321, 31]-code) [i]Truncation
2Linear OOA(2247, 32784, F2, 2, 31) (dual of [(32784, 2), 65321, 32]-NRT-code) [i]OOA Folding
3Linear OOA(2247, 21856, F2, 3, 31) (dual of [(21856, 3), 65321, 32]-NRT-code) [i]
4Linear OOA(2247, 16392, F2, 4, 31) (dual of [(16392, 4), 65321, 32]-NRT-code) [i]
5Linear OOA(2247, 13113, F2, 5, 31) (dual of [(13113, 5), 65318, 32]-NRT-code) [i]
6Linear OOA(2247, 10928, F2, 6, 31) (dual of [(10928, 6), 65321, 32]-NRT-code) [i]
7Linear OOA(2247, 9366, F2, 7, 31) (dual of [(9366, 7), 65315, 32]-NRT-code) [i]
8Linear OOA(2247, 8196, F2, 8, 31) (dual of [(8196, 8), 65321, 32]-NRT-code) [i]
9Linear OOA(2247, 4371, F2, 31, 31) (dual of [(4371, 31), 135254, 32]-NRT-code) [i]OOA Folding and Stacking with Additional Row