Information on Result #699797

Linear OA(12861, 2097179, F128, 19) (dual of [2097179, 2097118, 20]-code), using construction X applied to Ce(18) ⊂ Ce(11) based on
  1. linear OA(12855, 2097152, F128, 19) (dual of [2097152, 2097097, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(1286, 27, F128, 6) (dual of [27, 21, 7]-code or 27-arc in PG(5,128)), 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(3286, 2097179, S32, 19) [i]Discarding Parts of the Base for OAs
2OA(6472, 2097179, S64, 19) [i]
3Linear OOA(12861, 1546504, F128, 2, 19) (dual of [(1546504, 2), 3092947, 20]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12861, 1546504, F128, 3, 19) (dual of [(1546504, 3), 4639451, 20]-NRT-code) [i]
5Linear OOA(12861, 1546504, F128, 4, 19) (dual of [(1546504, 4), 6185955, 20]-NRT-code) [i]
6Digital (42, 61, 1546504)-net over F128 [i]
7Linear OOA(12861, 1048589, F128, 2, 19) (dual of [(1048589, 2), 2097117, 20]-NRT-code) [i]OOA Folding
8Linear OOA(12861, 699059, F128, 3, 19) (dual of [(699059, 3), 2097116, 20]-NRT-code) [i]