Information on Result #672725

Linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
  1. linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
  2. linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(2189, 8225, F2, 28) (dual of [8225, 8036, 29]-code) [i]Strength Reduction
2Linear OA(2190, 8226, F2, 29) (dual of [8226, 8036, 30]-code) [i]Code Embedding in Larger Space
3Linear OA(2191, 8227, F2, 29) (dual of [8227, 8036, 30]-code) [i]
4Linear OA(2192, 8228, F2, 29) (dual of [8228, 8036, 30]-code) [i]
5Linear OA(2193, 8229, F2, 29) (dual of [8229, 8036, 30]-code) [i]
6Linear OA(2194, 8230, F2, 29) (dual of [8230, 8036, 30]-code) [i]
7Linear OA(2188, 8224, F2, 28) (dual of [8224, 8036, 29]-code) [i]Truncation
8Linear OOA(2189, 4112, F2, 2, 29) (dual of [(4112, 2), 8035, 30]-NRT-code) [i]OOA Folding
9Linear OOA(2189, 2741, F2, 3, 29) (dual of [(2741, 3), 8034, 30]-NRT-code) [i]
10Linear OOA(2189, 2056, F2, 4, 29) (dual of [(2056, 4), 8035, 30]-NRT-code) [i]
11Linear OOA(2189, 1645, F2, 5, 29) (dual of [(1645, 5), 8036, 30]-NRT-code) [i]
12Linear OOA(2189, 1370, F2, 6, 29) (dual of [(1370, 6), 8031, 30]-NRT-code) [i]
13Linear OOA(2189, 1175, F2, 7, 29) (dual of [(1175, 7), 8036, 30]-NRT-code) [i]
14Linear OOA(2189, 1028, F2, 8, 29) (dual of [(1028, 8), 8035, 30]-NRT-code) [i]
15Linear OOA(2189, 587, F2, 29, 29) (dual of [(587, 29), 16834, 30]-NRT-code) [i]OOA Folding and Stacking with Additional Row