Information on Result #672209

Linear OA(2217, 2097185, F2, 21) (dual of [2097185, 2096968, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(2169, 2097153, F2, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(2216, 2097184, F2, 20) (dual of [2097184, 2096968, 21]-code) [i]Truncation
2Linear OOA(2217, 1048592, F2, 2, 21) (dual of [(1048592, 2), 2096967, 22]-NRT-code) [i]OOA Folding
3Linear OOA(2217, 699061, F2, 3, 21) (dual of [(699061, 3), 2096966, 22]-NRT-code) [i]
4Linear OOA(2217, 524296, F2, 4, 21) (dual of [(524296, 4), 2096967, 22]-NRT-code) [i]
5Linear OOA(2217, 419437, F2, 5, 21) (dual of [(419437, 5), 2096968, 22]-NRT-code) [i]
6Linear OOA(2217, 349530, F2, 6, 21) (dual of [(349530, 6), 2096963, 22]-NRT-code) [i]
7Linear OOA(2217, 262148, F2, 8, 21) (dual of [(262148, 8), 2096967, 22]-NRT-code) [i]
8Linear OOA(2217, 209718, F2, 21, 21) (dual of [(209718, 21), 4403861, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row