Information on Result #672320

Linear OA(2160, 524334, F2, 17) (dual of [524334, 524174, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
  1. linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(2115, 524289, F2, 13) (dual of [524289, 524174, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
  3. linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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(2159, 524333, F2, 16) (dual of [524333, 524174, 17]-code) [i]Truncation
2Linear OOA(2160, 262167, F2, 2, 17) (dual of [(262167, 2), 524174, 18]-NRT-code) [i]OOA Folding
3Linear OOA(2160, 174778, F2, 3, 17) (dual of [(174778, 3), 524174, 18]-NRT-code) [i]
4Linear OOA(2160, 131083, F2, 4, 17) (dual of [(131083, 4), 524172, 18]-NRT-code) [i]
5Linear OOA(2160, 104866, F2, 5, 17) (dual of [(104866, 5), 524170, 18]-NRT-code) [i]
6Linear OOA(2160, 87389, F2, 6, 17) (dual of [(87389, 6), 524174, 18]-NRT-code) [i]
7Linear OOA(2160, 74904, F2, 7, 17) (dual of [(74904, 7), 524168, 18]-NRT-code) [i]
8Linear OOA(2160, 65541, F2, 8, 17) (dual of [(65541, 8), 524168, 18]-NRT-code) [i]
9Linear OOA(2160, 65541, F2, 17, 17) (dual of [(65541, 17), 1114037, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row