Information on Result #699788

Linear OA(12857, 2097175, F128, 18) (dual of [2097175, 2097118, 19]-code), using construction X applied to Ce(17) ⊂ Ce(11) based on
  1. linear OA(12852, 2097152, F128, 18) (dual of [2097152, 2097100, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), 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
1OA(3280, 2097175, S32, 18) [i]Discarding Parts of the Base for OAs
2OA(6467, 2097175, S64, 18) [i]
3Linear OOA(12857, 1270479, F128, 2, 18) (dual of [(1270479, 2), 2540901, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12857, 1270479, F128, 3, 18) (dual of [(1270479, 3), 3811380, 19]-NRT-code) [i]
5Linear OOA(12857, 1270479, F128, 4, 18) (dual of [(1270479, 4), 5081859, 19]-NRT-code) [i]
6Digital (39, 57, 1270479)-net over F128 [i]
7Linear OOA(12857, 1048587, F128, 2, 18) (dual of [(1048587, 2), 2097117, 19]-NRT-code) [i]OOA Folding
8Linear OOA(12857, 699058, F128, 3, 18) (dual of [(699058, 3), 2097117, 19]-NRT-code) [i]
9Linear OOA(12857, 524293, F128, 4, 18) (dual of [(524293, 4), 2097115, 19]-NRT-code) [i]