Information on Result #672888

Linear OA(2227, 2077, F2, 41) (dual of [2077, 1850, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
  1. linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(2199, 2049, F2, 37) (dual of [2049, 1850, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
  3. linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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(2227, 2077, F2, 40) (dual of [2077, 1850, 41]-code) [i]Strength Reduction
2Linear OA(2228, 2078, F2, 41) (dual of [2078, 1850, 42]-code) [i]Code Embedding in Larger Space
3Linear OA(2229, 2079, F2, 41) (dual of [2079, 1850, 42]-code) [i]
4Linear OA(2230, 2080, F2, 41) (dual of [2080, 1850, 42]-code) [i]
5Linear OA(2231, 2081, F2, 41) (dual of [2081, 1850, 42]-code) [i]
6Linear OA(2226, 2076, F2, 40) (dual of [2076, 1850, 41]-code) [i]Truncation
7Linear OOA(2227, 1038, F2, 2, 41) (dual of [(1038, 2), 1849, 42]-NRT-code) [i]OOA Folding
8Linear OOA(2227, 692, F2, 3, 41) (dual of [(692, 3), 1849, 42]-NRT-code) [i]
9Linear OOA(2227, 519, F2, 4, 41) (dual of [(519, 4), 1849, 42]-NRT-code) [i]
10Linear OOA(2227, 415, F2, 5, 41) (dual of [(415, 5), 1848, 42]-NRT-code) [i]
11Linear OOA(2227, 346, F2, 6, 41) (dual of [(346, 6), 1849, 42]-NRT-code) [i]
12Linear OOA(2227, 296, F2, 7, 41) (dual of [(296, 7), 1845, 42]-NRT-code) [i]
13Linear OOA(2227, 259, F2, 8, 41) (dual of [(259, 8), 1845, 42]-NRT-code) [i]