Information on Result #672721

Linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,14]) based on
  1. linear OA(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  2. 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]
  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(2215, 8225, F2, 32) (dual of [8225, 8010, 33]-code) [i]Strength Reduction
2Linear OA(2216, 8226, F2, 33) (dual of [8226, 8010, 34]-code) [i]Code Embedding in Larger Space
3Linear OA(2217, 8227, F2, 33) (dual of [8227, 8010, 34]-code) [i]
4Linear OA(2218, 8228, F2, 33) (dual of [8228, 8010, 34]-code) [i]
5Linear OA(2219, 8229, F2, 33) (dual of [8229, 8010, 34]-code) [i]
6Linear OA(2220, 8230, F2, 33) (dual of [8230, 8010, 34]-code) [i]
7Linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code) [i]Truncation
8Linear OOA(2215, 4112, F2, 2, 33) (dual of [(4112, 2), 8009, 34]-NRT-code) [i]OOA Folding
9Linear OOA(2215, 2741, F2, 3, 33) (dual of [(2741, 3), 8008, 34]-NRT-code) [i]
10Linear OOA(2215, 2056, F2, 4, 33) (dual of [(2056, 4), 8009, 34]-NRT-code) [i]
11Linear OOA(2215, 1645, F2, 5, 33) (dual of [(1645, 5), 8010, 34]-NRT-code) [i]
12Linear OOA(2215, 1370, F2, 6, 33) (dual of [(1370, 6), 8005, 34]-NRT-code) [i]
13Linear OOA(2215, 1175, F2, 7, 33) (dual of [(1175, 7), 8010, 34]-NRT-code) [i]
14Linear OOA(2215, 1028, F2, 8, 33) (dual of [(1028, 8), 8009, 34]-NRT-code) [i]