Information on Result #672380

Linear OA(2151, 262177, F2, 17) (dual of [262177, 262026, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
  1. linear OA(2145, 262145, F2, 17) (dual of [262145, 262000, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(2109, 262145, F2, 13) (dual of [262145, 262036, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 236−1, 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(2150, 262176, F2, 16) (dual of [262176, 262026, 17]-code) [i]Truncation
2Linear OOA(2151, 131088, F2, 2, 17) (dual of [(131088, 2), 262025, 18]-NRT-code) [i]OOA Folding
3Linear OOA(2151, 87392, F2, 3, 17) (dual of [(87392, 3), 262025, 18]-NRT-code) [i]
4Linear OOA(2151, 65544, F2, 4, 17) (dual of [(65544, 4), 262025, 18]-NRT-code) [i]
5Linear OOA(2151, 52435, F2, 5, 17) (dual of [(52435, 5), 262024, 18]-NRT-code) [i]
6Linear OOA(2151, 43696, F2, 6, 17) (dual of [(43696, 6), 262025, 18]-NRT-code) [i]
7Linear OOA(2151, 37453, F2, 7, 17) (dual of [(37453, 7), 262020, 18]-NRT-code) [i]
8Linear OOA(2151, 32772, F2, 8, 17) (dual of [(32772, 8), 262025, 18]-NRT-code) [i]
9Linear OOA(2151, 32772, F2, 17, 17) (dual of [(32772, 17), 556973, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row