Information on Result #672780

Linear OA(2124, 8224, F2, 19) (dual of [8224, 8100, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2118, 8192, F2, 19) (dual of [8192, 8074, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(292, 8192, F2, 15) (dual of [8192, 8100, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(2124, 8224, F2, 18) (dual of [8224, 8100, 19]-code) [i]Strength Reduction
2Linear OA(2125, 8225, F2, 19) (dual of [8225, 8100, 20]-code) [i]Code Embedding in Larger Space
3Linear OA(2126, 8226, F2, 19) (dual of [8226, 8100, 20]-code) [i]
4Linear OA(2123, 8223, F2, 18) (dual of [8223, 8100, 19]-code) [i]Truncation
5Linear OOA(2124, 4112, F2, 2, 19) (dual of [(4112, 2), 8100, 20]-NRT-code) [i]OOA Folding
6Linear OOA(2124, 2741, F2, 3, 19) (dual of [(2741, 3), 8099, 20]-NRT-code) [i]
7Linear OOA(2124, 2056, F2, 4, 19) (dual of [(2056, 4), 8100, 20]-NRT-code) [i]
8Linear OOA(2124, 1644, F2, 5, 19) (dual of [(1644, 5), 8096, 20]-NRT-code) [i]
9Linear OOA(2124, 1370, F2, 6, 19) (dual of [(1370, 6), 8096, 20]-NRT-code) [i]
10Linear OOA(2124, 1174, F2, 7, 19) (dual of [(1174, 7), 8094, 20]-NRT-code) [i]
11Linear OOA(2124, 1028, F2, 8, 19) (dual of [(1028, 8), 8100, 20]-NRT-code) [i]
12Linear OOA(2124, 913, F2, 19, 19) (dual of [(913, 19), 17223, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row