Information on Result #672910

Linear OA(2116, 2065, F2, 21) (dual of [2065, 1949, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(289, 2049, F2, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  3. linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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(2115, 2064, F2, 20) (dual of [2064, 1949, 21]-code) [i]Truncation
2Linear OOA(2116, 413, F2, 5, 21) (dual of [(413, 5), 1949, 22]-NRT-code) [i]OOA Folding
3Linear OOA(2116, 344, F2, 6, 21) (dual of [(344, 6), 1948, 22]-NRT-code) [i]
4Linear OOA(2116, 295, F2, 7, 21) (dual of [(295, 7), 1949, 22]-NRT-code) [i]
5Linear OOA(2116, 258, F2, 8, 21) (dual of [(258, 8), 1948, 22]-NRT-code) [i]