Information on Result #672406

Linear OA(292, 262164, F2, 11) (dual of [262164, 262072, 12]-code), using construction X4 applied to Ce(10) ⊂ Ce(8) based on
  1. linear OA(291, 262144, F2, 11) (dual of [262144, 262053, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
  2. linear OA(273, 262144, F2, 9) (dual of [262144, 262071, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(219, 20, F2, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,2)), using
  4. linear OA(21, 20, F2, 1) (dual of [20, 19, 2]-code), 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(292, 262164, F2, 10) (dual of [262164, 262072, 11]-code) [i]Strength Reduction
2Linear OA(293, 262165, F2, 11) (dual of [262165, 262072, 12]-code) [i]Code Embedding in Larger Space
3Linear OA(294, 262166, F2, 11) (dual of [262166, 262072, 12]-code) [i]
4Linear OA(295, 262167, F2, 11) (dual of [262167, 262072, 12]-code) [i]
5Linear OA(291, 262163, F2, 10) (dual of [262163, 262072, 11]-code) [i]Truncation
6Linear OOA(292, 131082, F2, 2, 11) (dual of [(131082, 2), 262072, 12]-NRT-code) [i]OOA Folding
7Linear OOA(292, 87388, F2, 3, 11) (dual of [(87388, 3), 262072, 12]-NRT-code) [i]
8Linear OOA(292, 65541, F2, 4, 11) (dual of [(65541, 4), 262072, 12]-NRT-code) [i]