Information on Result #699799

Linear OA(12855, 2097179, F128, 17) (dual of [2097179, 2097124, 18]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
  1. linear OA(12849, 2097152, F128, 17) (dual of [2097152, 2097103, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  2. linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(3277, 2097179, S32, 17) [i]Discarding Parts of the Base for OAs
2Linear OOA(12855, 1949474, F128, 2, 17) (dual of [(1949474, 2), 3898893, 18]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(12855, 1949474, F128, 3, 17) (dual of [(1949474, 3), 5848367, 18]-NRT-code) [i]
4Linear OOA(12855, 1949474, F128, 4, 17) (dual of [(1949474, 4), 7797841, 18]-NRT-code) [i]
5Digital (38, 55, 1949474)-net over F128 [i]
6Linear OOA(12855, 1048589, F128, 2, 17) (dual of [(1048589, 2), 2097123, 18]-NRT-code) [i]OOA Folding
7Linear OOA(12855, 699059, F128, 3, 17) (dual of [(699059, 3), 2097122, 18]-NRT-code) [i]
8Linear OOA(12855, 262147, F128, 17, 17) (dual of [(262147, 17), 4456444, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row