Information on Result #699814

Linear OA(12860, 2097187, F128, 18) (dual of [2097187, 2097127, 19]-code), using construction X applied to Ce(17) ⊂ Ce(8) 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(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(1288, 35, F128, 8) (dual of [35, 27, 9]-code or 35-arc in PG(7,128)), 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
1Linear OOA(12860, 2097187, F128, 2, 18) (dual of [(2097187, 2), 4194314, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12860, 2097187, F128, 3, 18) (dual of [(2097187, 3), 6291501, 19]-NRT-code) [i]
3Linear OOA(12860, 2097187, F128, 4, 18) (dual of [(2097187, 4), 8388688, 19]-NRT-code) [i]
4Digital (42, 60, 2097187)-net over F128 [i]
5Linear OOA(12860, 1048593, F128, 2, 18) (dual of [(1048593, 2), 2097126, 19]-NRT-code) [i]OOA Folding
6Linear OOA(12860, 699062, F128, 3, 18) (dual of [(699062, 3), 2097126, 19]-NRT-code) [i]
7Linear OOA(12860, 524296, F128, 4, 18) (dual of [(524296, 4), 2097124, 19]-NRT-code) [i]