Information on Result #699781

Linear OA(12841, 2097171, F128, 13) (dual of [2097171, 2097130, 14]-code), using construction X applied to Ce(12) ⊂ Ce(7) based on
  1. 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]
  2. linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(1284, 19, F128, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,128)), 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(1672, 2097171, S16, 13) [i]Discarding Parts of the Base for OAs
2OA(3258, 2097171, S32, 13) [i]
3OA(6448, 2097171, S64, 13) [i]
4Linear OOA(12841, 1777424, F128, 2, 13) (dual of [(1777424, 2), 3554807, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
5Linear OOA(12841, 1777424, F128, 3, 13) (dual of [(1777424, 3), 5332231, 14]-NRT-code) [i]
6Linear OOA(12841, 1777424, F128, 4, 13) (dual of [(1777424, 4), 7109655, 14]-NRT-code) [i]
7Digital (28, 41, 1777424)-net over F128 [i]
8Linear OOA(12841, 1048585, F128, 2, 13) (dual of [(1048585, 2), 2097129, 14]-NRT-code) [i]OOA Folding
9Linear OOA(12841, 699057, F128, 3, 13) (dual of [(699057, 3), 2097130, 14]-NRT-code) [i]
10Linear OOA(12841, 349528, F128, 13, 13) (dual of [(349528, 13), 4543823, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row