Information on Result #672614

Linear OA(2232, 32800, F2, 31) (dual of [32800, 32568, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
  1. linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, 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(2231, 32799, F2, 30) (dual of [32799, 32568, 31]-code) [i]Truncation
2Linear OOA(2232, 16400, F2, 2, 31) (dual of [(16400, 2), 32568, 32]-NRT-code) [i]OOA Folding
3Linear OOA(2232, 10933, F2, 3, 31) (dual of [(10933, 3), 32567, 32]-NRT-code) [i]
4Linear OOA(2232, 8200, F2, 4, 31) (dual of [(8200, 4), 32568, 32]-NRT-code) [i]
5Linear OOA(2232, 6560, F2, 5, 31) (dual of [(6560, 5), 32568, 32]-NRT-code) [i]
6Linear OOA(2232, 5466, F2, 6, 31) (dual of [(5466, 6), 32564, 32]-NRT-code) [i]
7Linear OOA(2232, 4685, F2, 7, 31) (dual of [(4685, 7), 32563, 32]-NRT-code) [i]
8Linear OOA(2232, 4100, F2, 8, 31) (dual of [(4100, 8), 32568, 32]-NRT-code) [i]
9Linear OOA(2232, 2186, F2, 31, 31) (dual of [(2186, 31), 67534, 32]-NRT-code) [i]OOA Folding and Stacking with Additional Row