Information on Result #672706

Linear OA(2134, 16419, F2, 19) (dual of [16419, 16285, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. linear OA(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(299, 16384, F2, 15) (dual of [16384, 16285, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
  3. linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-cap in PG(6,2)), 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(2134, 16419, F2, 18) (dual of [16419, 16285, 19]-code) [i]Strength Reduction
2Linear OA(2135, 16420, F2, 19) (dual of [16420, 16285, 20]-code) [i]Code Embedding in Larger Space
3Linear OA(2133, 16418, F2, 18) (dual of [16418, 16285, 19]-code) [i]Truncation
4Linear OOA(2134, 8209, F2, 2, 19) (dual of [(8209, 2), 16284, 20]-NRT-code) [i]OOA Folding
5Linear OOA(2134, 5473, F2, 3, 19) (dual of [(5473, 3), 16285, 20]-NRT-code) [i]
6Linear OOA(2134, 1824, F2, 19, 19) (dual of [(1824, 19), 34522, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row