Information on Result #672441

Linear OA(2144, 131114, F2, 17) (dual of [131114, 130970, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
  1. linear OA(2137, 131073, F2, 17) (dual of [131073, 130936, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
  3. linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-cap in PG(6,2)), 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 OA(2143, 131113, F2, 16) (dual of [131113, 130970, 17]-code) [i]Truncation
2Linear OOA(2144, 65557, F2, 2, 17) (dual of [(65557, 2), 130970, 18]-NRT-code) [i]OOA Folding
3Linear OOA(2144, 43704, F2, 3, 17) (dual of [(43704, 3), 130968, 18]-NRT-code) [i]
4Linear OOA(2144, 32778, F2, 4, 17) (dual of [(32778, 4), 130968, 18]-NRT-code) [i]
5Linear OOA(2144, 26222, F2, 5, 17) (dual of [(26222, 5), 130966, 18]-NRT-code) [i]
6Linear OOA(2144, 21852, F2, 6, 17) (dual of [(21852, 6), 130968, 18]-NRT-code) [i]
7Linear OOA(2144, 18730, F2, 7, 17) (dual of [(18730, 7), 130966, 18]-NRT-code) [i]
8Linear OOA(2144, 16389, F2, 8, 17) (dual of [(16389, 8), 130968, 18]-NRT-code) [i]
9Linear OOA(2144, 16389, F2, 17, 17) (dual of [(16389, 17), 278469, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row