Information on Result #672776

Linear OA(2228, 8224, F2, 35) (dual of [8224, 7996, 36]-code), using construction X applied to Ce(34) ⊂ Ce(30) based on
  1. linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  2. linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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(2228, 8224, F2, 34) (dual of [8224, 7996, 35]-code) [i]Strength Reduction
2Linear OA(2229, 8225, F2, 35) (dual of [8225, 7996, 36]-code) [i]Code Embedding in Larger Space
3Linear OA(2230, 8226, F2, 35) (dual of [8226, 7996, 36]-code) [i]
4Linear OA(2231, 8227, F2, 35) (dual of [8227, 7996, 36]-code) [i]
5Linear OA(2232, 8228, F2, 35) (dual of [8228, 7996, 36]-code) [i]
6Linear OA(2233, 8229, F2, 35) (dual of [8229, 7996, 36]-code) [i]
7Linear OA(2227, 8223, F2, 34) (dual of [8223, 7996, 35]-code) [i]Truncation
8Linear OOA(2228, 4112, F2, 2, 35) (dual of [(4112, 2), 7996, 36]-NRT-code) [i]OOA Folding
9Linear OOA(2228, 2741, F2, 3, 35) (dual of [(2741, 3), 7995, 36]-NRT-code) [i]
10Linear OOA(2228, 2056, F2, 4, 35) (dual of [(2056, 4), 7996, 36]-NRT-code) [i]
11Linear OOA(2228, 1644, F2, 5, 35) (dual of [(1644, 5), 7992, 36]-NRT-code) [i]
12Linear OOA(2228, 1370, F2, 6, 35) (dual of [(1370, 6), 7992, 36]-NRT-code) [i]
13Linear OOA(2228, 1174, F2, 7, 35) (dual of [(1174, 7), 7990, 36]-NRT-code) [i]
14Linear OOA(2228, 1028, F2, 8, 35) (dual of [(1028, 8), 7996, 36]-NRT-code) [i]