Information on Result #672558

Linear OA(2248, 32806, F2, 33) (dual of [32806, 32558, 34]-code), using construction X applied to C([0,16]) ⊂ C([0,14]) based on
  1. linear OA(2241, 32769, F2, 33) (dual of [32769, 32528, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  2. linear OA(2211, 32769, F2, 29) (dual of [32769, 32558, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
  3. linear OA(27, 37, F2, 3) (dual of [37, 30, 4]-code or 37-cap in PG(6,2)), 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(2248, 32806, F2, 32) (dual of [32806, 32558, 33]-code) [i]Strength Reduction
2Linear OA(2249, 32807, F2, 33) (dual of [32807, 32558, 34]-code) [i]Code Embedding in Larger Space
3Linear OA(2250, 32808, F2, 33) (dual of [32808, 32558, 34]-code) [i]
4Linear OA(2251, 32809, F2, 33) (dual of [32809, 32558, 34]-code) [i]
5Linear OA(2252, 32810, F2, 33) (dual of [32810, 32558, 34]-code) [i]
6Linear OA(2247, 32805, F2, 32) (dual of [32805, 32558, 33]-code) [i]Truncation
7Linear OOA(2248, 16403, F2, 2, 33) (dual of [(16403, 2), 32558, 34]-NRT-code) [i]OOA Folding
8Linear OOA(2248, 10935, F2, 3, 33) (dual of [(10935, 3), 32557, 34]-NRT-code) [i]
9Linear OOA(2248, 8201, F2, 4, 33) (dual of [(8201, 4), 32556, 34]-NRT-code) [i]
10Linear OOA(2248, 6561, F2, 5, 33) (dual of [(6561, 5), 32557, 34]-NRT-code) [i]
11Linear OOA(2248, 5467, F2, 6, 33) (dual of [(5467, 6), 32554, 34]-NRT-code) [i]
12Linear OOA(2248, 4686, F2, 7, 33) (dual of [(4686, 7), 32554, 34]-NRT-code) [i]