Information on Result #672705

Linear OA(2133, 16416, F2, 19) (dual of [16416, 16283, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, 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(2132, 16415, F2, 18) (dual of [16415, 16283, 19]-code) [i]Truncation
2Linear OOA(2133, 8208, F2, 2, 19) (dual of [(8208, 2), 16283, 20]-NRT-code) [i]OOA Folding
3Linear OOA(2133, 5472, F2, 3, 19) (dual of [(5472, 3), 16283, 20]-NRT-code) [i]
4Linear OOA(2133, 4104, F2, 4, 19) (dual of [(4104, 4), 16283, 20]-NRT-code) [i]
5Linear OOA(2133, 3283, F2, 5, 19) (dual of [(3283, 5), 16282, 20]-NRT-code) [i]
6Linear OOA(2133, 2736, F2, 6, 19) (dual of [(2736, 6), 16283, 20]-NRT-code) [i]
7Linear OOA(2133, 2345, F2, 7, 19) (dual of [(2345, 7), 16282, 20]-NRT-code) [i]
8Linear OOA(2133, 2052, F2, 8, 19) (dual of [(2052, 8), 16283, 20]-NRT-code) [i]
9Linear OOA(2133, 1823, F2, 19, 19) (dual of [(1823, 19), 34504, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row