Information on Result #672419

Linear OA(2169, 262176, F2, 19) (dual of [262176, 262007, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(2127, 262144, F2, 15) (dual of [262144, 262017, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(2168, 262175, F2, 18) (dual of [262175, 262007, 19]-code) [i]Truncation
2Linear OOA(2169, 131088, F2, 2, 19) (dual of [(131088, 2), 262007, 20]-NRT-code) [i]OOA Folding
3Linear OOA(2169, 87392, F2, 3, 19) (dual of [(87392, 3), 262007, 20]-NRT-code) [i]
4Linear OOA(2169, 65544, F2, 4, 19) (dual of [(65544, 4), 262007, 20]-NRT-code) [i]
5Linear OOA(2169, 52435, F2, 5, 19) (dual of [(52435, 5), 262006, 20]-NRT-code) [i]
6Linear OOA(2169, 43696, F2, 6, 19) (dual of [(43696, 6), 262007, 20]-NRT-code) [i]
7Linear OOA(2169, 37453, F2, 7, 19) (dual of [(37453, 7), 262002, 20]-NRT-code) [i]
8Linear OOA(2169, 32772, F2, 8, 19) (dual of [(32772, 8), 262007, 20]-NRT-code) [i]
9Linear OOA(2169, 29130, F2, 19, 19) (dual of [(29130, 19), 553301, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row