Information on Result #672481

Linear OA(2126, 131104, F2, 15) (dual of [131104, 130978, 16]-code), using construction X applied to Ce(14) ⊂ Ce(10) based on
  1. linear OA(2120, 131072, F2, 15) (dual of [131072, 130952, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  2. linear OA(286, 131072, F2, 11) (dual of [131072, 130986, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 131071 = 217−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(2125, 131103, F2, 14) (dual of [131103, 130978, 15]-code) [i]Truncation
2Linear OOA(2126, 65552, F2, 2, 15) (dual of [(65552, 2), 130978, 16]-NRT-code) [i]OOA Folding
3Linear OOA(2126, 43701, F2, 3, 15) (dual of [(43701, 3), 130977, 16]-NRT-code) [i]
4Linear OOA(2126, 32776, F2, 4, 15) (dual of [(32776, 4), 130978, 16]-NRT-code) [i]
5Linear OOA(2126, 26220, F2, 5, 15) (dual of [(26220, 5), 130974, 16]-NRT-code) [i]
6Linear OOA(2126, 21850, F2, 6, 15) (dual of [(21850, 6), 130974, 16]-NRT-code) [i]
7Linear OOA(2126, 18729, F2, 7, 15) (dual of [(18729, 7), 130977, 16]-NRT-code) [i]
8Linear OOA(2126, 18729, F2, 8, 15) (dual of [(18729, 8), 149706, 16]-NRT-code) [i]OOA Folding and Stacking with Additional Row
9Linear OOA(2126, 18729, F2, 15, 15) (dual of [(18729, 15), 280809, 16]-NRT-code) [i]