Information on Result #699798

Linear OA(12858, 2097179, F128, 18) (dual of [2097179, 2097121, 19]-code), using construction X applied to Ce(17) ⊂ Ce(10) 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(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(3282, 2097179, S32, 18) [i]Discarding Parts of the Base for OAs
2OA(6468, 2097179, S64, 18) [i]
3Linear OOA(12858, 1720556, F128, 2, 18) (dual of [(1720556, 2), 3441054, 19]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(12858, 1720556, F128, 3, 18) (dual of [(1720556, 3), 5161610, 19]-NRT-code) [i]
5Linear OOA(12858, 1720556, F128, 4, 18) (dual of [(1720556, 4), 6882166, 19]-NRT-code) [i]
6Digital (40, 58, 1720556)-net over F128 [i]
7Linear OOA(12858, 1048589, F128, 2, 18) (dual of [(1048589, 2), 2097120, 19]-NRT-code) [i]OOA Folding
8Linear OOA(12858, 699059, F128, 3, 18) (dual of [(699059, 3), 2097119, 19]-NRT-code) [i]
9Linear OOA(12858, 524294, F128, 4, 18) (dual of [(524294, 4), 2097118, 19]-NRT-code) [i]