Information on Result #672778

Linear OA(2176, 8224, F2, 27) (dual of [8224, 8048, 28]-code), using construction X applied to Ce(26) ⊂ Ce(22) based on
  1. linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(2144, 8192, F2, 23) (dual of [8192, 8048, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(2176, 8224, F2, 26) (dual of [8224, 8048, 27]-code) [i]Strength Reduction
2Linear OA(2177, 8225, F2, 27) (dual of [8225, 8048, 28]-code) [i]Code Embedding in Larger Space
3Linear OA(2178, 8226, F2, 27) (dual of [8226, 8048, 28]-code) [i]
4Linear OA(2179, 8227, F2, 27) (dual of [8227, 8048, 28]-code) [i]
5Linear OA(2180, 8228, F2, 27) (dual of [8228, 8048, 28]-code) [i]
6Linear OA(2181, 8229, F2, 27) (dual of [8229, 8048, 28]-code) [i]
7Linear OA(2175, 8223, F2, 26) (dual of [8223, 8048, 27]-code) [i]Truncation
8Linear OOA(2176, 4112, F2, 2, 27) (dual of [(4112, 2), 8048, 28]-NRT-code) [i]OOA Folding
9Linear OOA(2176, 2741, F2, 3, 27) (dual of [(2741, 3), 8047, 28]-NRT-code) [i]
10Linear OOA(2176, 2056, F2, 4, 27) (dual of [(2056, 4), 8048, 28]-NRT-code) [i]
11Linear OOA(2176, 1644, F2, 5, 27) (dual of [(1644, 5), 8044, 28]-NRT-code) [i]
12Linear OOA(2176, 1370, F2, 6, 27) (dual of [(1370, 6), 8044, 28]-NRT-code) [i]
13Linear OOA(2176, 1174, F2, 7, 27) (dual of [(1174, 7), 8042, 28]-NRT-code) [i]
14Linear OOA(2176, 1028, F2, 8, 27) (dual of [(1028, 8), 8048, 28]-NRT-code) [i]
15Linear OOA(2176, 632, F2, 27, 27) (dual of [(632, 27), 16888, 28]-NRT-code) [i]OOA Folding and Stacking with Additional Row