Information on Result #672700

Linear OA(2218, 16419, F2, 31) (dual of [16419, 16201, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
  1. linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(2218, 16419, F2, 30) (dual of [16419, 16201, 31]-code) [i]Strength Reduction
2Linear OA(2219, 16420, F2, 31) (dual of [16420, 16201, 32]-code) [i]Code Embedding in Larger Space
3Linear OA(2220, 16421, F2, 31) (dual of [16421, 16201, 32]-code) [i]
4Linear OA(2221, 16422, F2, 31) (dual of [16422, 16201, 32]-code) [i]
5Linear OA(2222, 16423, F2, 31) (dual of [16423, 16201, 32]-code) [i]
6Linear OA(2217, 16418, F2, 30) (dual of [16418, 16201, 31]-code) [i]Truncation
7Linear OOA(2218, 8209, F2, 2, 31) (dual of [(8209, 2), 16200, 32]-NRT-code) [i]OOA Folding
8Linear OOA(2218, 5473, F2, 3, 31) (dual of [(5473, 3), 16201, 32]-NRT-code) [i]