Information on Result #672653

Linear OA(2147, 16417, F2, 21) (dual of [16417, 16270, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(2141, 16385, F2, 21) (dual of [16385, 16244, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(2113, 16385, F2, 17) (dual of [16385, 16272, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, 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(2146, 16416, F2, 20) (dual of [16416, 16270, 21]-code) [i]Truncation
2Linear OOA(2147, 8208, F2, 2, 21) (dual of [(8208, 2), 16269, 22]-NRT-code) [i]OOA Folding
3Linear OOA(2147, 5472, F2, 3, 21) (dual of [(5472, 3), 16269, 22]-NRT-code) [i]
4Linear OOA(2147, 4104, F2, 4, 21) (dual of [(4104, 4), 16269, 22]-NRT-code) [i]
5Linear OOA(2147, 3283, F2, 5, 21) (dual of [(3283, 5), 16268, 22]-NRT-code) [i]
6Linear OOA(2147, 2736, F2, 6, 21) (dual of [(2736, 6), 16269, 22]-NRT-code) [i]
7Linear OOA(2147, 2345, F2, 7, 21) (dual of [(2345, 7), 16268, 22]-NRT-code) [i]
8Linear OOA(2147, 2052, F2, 8, 21) (dual of [(2052, 8), 16269, 22]-NRT-code) [i]
9Linear OOA(2147, 1641, F2, 21, 21) (dual of [(1641, 21), 34314, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row