Information on Result #672506

Linear OA(2135, 65569, F2, 17) (dual of [65569, 65434, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
  1. linear OA(2129, 65537, F2, 17) (dual of [65537, 65408, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
  3. linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2134, 65568, F2, 16) (dual of [65568, 65434, 17]-code) [i]Truncation
2Linear OOA(2135, 32784, F2, 2, 17) (dual of [(32784, 2), 65433, 18]-NRT-code) [i]OOA Folding
3Linear OOA(2135, 21856, F2, 3, 17) (dual of [(21856, 3), 65433, 18]-NRT-code) [i]
4Linear OOA(2135, 16392, F2, 4, 17) (dual of [(16392, 4), 65433, 18]-NRT-code) [i]
5Linear OOA(2135, 13113, F2, 5, 17) (dual of [(13113, 5), 65430, 18]-NRT-code) [i]
6Linear OOA(2135, 10928, F2, 6, 17) (dual of [(10928, 6), 65433, 18]-NRT-code) [i]
7Linear OOA(2135, 9367, F2, 7, 17) (dual of [(9367, 7), 65434, 18]-NRT-code) [i]
8Linear OOA(2135, 8196, F2, 8, 17) (dual of [(8196, 8), 65433, 18]-NRT-code) [i]
9Linear OOA(2135, 8196, F2, 17, 17) (dual of [(8196, 17), 139197, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row