Information on Result #672699

Linear OA(2217, 16416, F2, 31) (dual of [16416, 16199, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
  1. linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, 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(2216, 16415, F2, 30) (dual of [16415, 16199, 31]-code) [i]Truncation
2Linear OOA(2217, 8208, F2, 2, 31) (dual of [(8208, 2), 16199, 32]-NRT-code) [i]OOA Folding
3Linear OOA(2217, 5472, F2, 3, 31) (dual of [(5472, 3), 16199, 32]-NRT-code) [i]
4Linear OOA(2217, 4104, F2, 4, 31) (dual of [(4104, 4), 16199, 32]-NRT-code) [i]
5Linear OOA(2217, 3283, F2, 5, 31) (dual of [(3283, 5), 16198, 32]-NRT-code) [i]
6Linear OOA(2217, 2736, F2, 6, 31) (dual of [(2736, 6), 16199, 32]-NRT-code) [i]
7Linear OOA(2217, 2345, F2, 7, 31) (dual of [(2345, 7), 16198, 32]-NRT-code) [i]
8Linear OOA(2217, 2052, F2, 8, 31) (dual of [(2052, 8), 16199, 32]-NRT-code) [i]
9Linear OOA(2217, 1094, F2, 31, 31) (dual of [(1094, 31), 33697, 32]-NRT-code) [i]OOA Folding and Stacking with Additional Row