Information on Result #672786

Linear OA(2209, 8244, F2, 31) (dual of [8244, 8035, 32]-code), using construction X applied to Ce(30) ⊂ Ce(24) based on
  1. linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(213, 52, F2, 5) (dual of [52, 39, 6]-code), 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(2209, 8244, F2, 30) (dual of [8244, 8035, 31]-code) [i]Strength Reduction
2Linear OA(2210, 8245, F2, 31) (dual of [8245, 8035, 32]-code) [i]Code Embedding in Larger Space
3Linear OA(2208, 8243, F2, 30) (dual of [8243, 8035, 31]-code) [i]Truncation
4Linear OOA(2209, 4122, F2, 2, 31) (dual of [(4122, 2), 8035, 32]-NRT-code) [i]OOA Folding
5Linear OOA(2209, 2748, F2, 3, 31) (dual of [(2748, 3), 8035, 32]-NRT-code) [i]
6Linear OOA(2209, 2061, F2, 4, 31) (dual of [(2061, 4), 8035, 32]-NRT-code) [i]
7Linear OOA(2209, 1374, F2, 6, 31) (dual of [(1374, 6), 8035, 32]-NRT-code) [i]