Information on Result #672435

Linear OA(2177, 131105, F2, 21) (dual of [131105, 130928, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(2171, 131073, F2, 21) (dual of [131073, 130902, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(2137, 131073, F2, 17) (dual of [131073, 130936, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, 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(2176, 131104, F2, 20) (dual of [131104, 130928, 21]-code) [i]Truncation
2Linear OOA(2177, 65552, F2, 2, 21) (dual of [(65552, 2), 130927, 22]-NRT-code) [i]OOA Folding
3Linear OOA(2177, 43701, F2, 3, 21) (dual of [(43701, 3), 130926, 22]-NRT-code) [i]
4Linear OOA(2177, 32776, F2, 4, 21) (dual of [(32776, 4), 130927, 22]-NRT-code) [i]
5Linear OOA(2177, 26221, F2, 5, 21) (dual of [(26221, 5), 130928, 22]-NRT-code) [i]
6Linear OOA(2177, 21850, F2, 6, 21) (dual of [(21850, 6), 130923, 22]-NRT-code) [i]
7Linear OOA(2177, 18729, F2, 7, 21) (dual of [(18729, 7), 130926, 22]-NRT-code) [i]
8Linear OOA(2177, 16388, F2, 8, 21) (dual of [(16388, 8), 130927, 22]-NRT-code) [i]
9Linear OOA(2177, 13110, F2, 21, 21) (dual of [(13110, 21), 275133, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row