Information on Result #672572

Linear OA(2157, 32801, F2, 21) (dual of [32801, 32644, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(2151, 32769, F2, 21) (dual of [32769, 32618, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(2121, 32769, F2, 17) (dual of [32769, 32648, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 230−1, 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(2156, 32800, F2, 20) (dual of [32800, 32644, 21]-code) [i]Truncation
2Linear OOA(2157, 16400, F2, 2, 21) (dual of [(16400, 2), 32643, 22]-NRT-code) [i]OOA Folding
3Linear OOA(2157, 10933, F2, 3, 21) (dual of [(10933, 3), 32642, 22]-NRT-code) [i]
4Linear OOA(2157, 8200, F2, 4, 21) (dual of [(8200, 4), 32643, 22]-NRT-code) [i]
5Linear OOA(2157, 6560, F2, 5, 21) (dual of [(6560, 5), 32643, 22]-NRT-code) [i]
6Linear OOA(2157, 5466, F2, 6, 21) (dual of [(5466, 6), 32639, 22]-NRT-code) [i]
7Linear OOA(2157, 4685, F2, 7, 21) (dual of [(4685, 7), 32638, 22]-NRT-code) [i]
8Linear OOA(2157, 4100, F2, 8, 21) (dual of [(4100, 8), 32643, 22]-NRT-code) [i]
9Linear OOA(2157, 3280, F2, 21, 21) (dual of [(3280, 21), 68723, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row