Information on Result #672903

Linear OA(2161, 2077, F2, 29) (dual of [2077, 1916, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
  1. linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
  2. linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (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(2161, 2077, F2, 28) (dual of [2077, 1916, 29]-code) [i]Strength Reduction
2Linear OA(2162, 2078, F2, 29) (dual of [2078, 1916, 30]-code) [i]Code Embedding in Larger Space
3Linear OA(2163, 2079, F2, 29) (dual of [2079, 1916, 30]-code) [i]
4Linear OA(2164, 2080, F2, 29) (dual of [2080, 1916, 30]-code) [i]
5Linear OA(2165, 2081, F2, 29) (dual of [2081, 1916, 30]-code) [i]
6Linear OA(2160, 2076, F2, 28) (dual of [2076, 1916, 29]-code) [i]Truncation
7Linear OOA(2161, 1038, F2, 2, 29) (dual of [(1038, 2), 1915, 30]-NRT-code) [i]OOA Folding
8Linear OOA(2161, 692, F2, 3, 29) (dual of [(692, 3), 1915, 30]-NRT-code) [i]
9Linear OOA(2161, 519, F2, 4, 29) (dual of [(519, 4), 1915, 30]-NRT-code) [i]
10Linear OOA(2161, 415, F2, 5, 29) (dual of [(415, 5), 1914, 30]-NRT-code) [i]
11Linear OOA(2161, 346, F2, 6, 29) (dual of [(346, 6), 1915, 30]-NRT-code) [i]
12Linear OOA(2161, 296, F2, 7, 29) (dual of [(296, 7), 1911, 30]-NRT-code) [i]
13Linear OOA(2161, 259, F2, 8, 29) (dual of [(259, 8), 1911, 30]-NRT-code) [i]