Information on Result #699796

Linear OA(12864, 2097179, F128, 20) (dual of [2097179, 2097115, 21]-code), using construction X applied to Ce(19) ⊂ Ce(12) based on
  1. linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(3290, 2097179, S32, 20) [i]Discarding Parts of the Base for OAs
2OA(6475, 2097179, S64, 20) [i]
3Linear OOA(12864, 1411103, F128, 2, 20) (dual of [(1411103, 2), 2822142, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12864, 1411103, F128, 3, 20) (dual of [(1411103, 3), 4233245, 21]-NRT-code) [i]
5Linear OOA(12864, 1411103, F128, 4, 20) (dual of [(1411103, 4), 5644348, 21]-NRT-code) [i]
6Digital (44, 64, 1411103)-net over F128 [i]
7Linear OOA(12864, 1048589, F128, 2, 20) (dual of [(1048589, 2), 2097114, 21]-NRT-code) [i]OOA Folding
8Linear OOA(12864, 699059, F128, 3, 20) (dual of [(699059, 3), 2097113, 21]-NRT-code) [i]
9Linear OOA(12864, 524294, F128, 4, 20) (dual of [(524294, 4), 2097112, 21]-NRT-code) [i]