Information on Result #672744

Linear OA(2236, 8206, F2, 37) (dual of [8206, 7970, 38]-code), using construction X applied to Ce(36) ⊂ Ce(34) based on
  1. linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  3. linear OA(21, 14, F2, 1) (dual of [14, 13, 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(2236, 8206, F2, 36) (dual of [8206, 7970, 37]-code) [i]Strength Reduction
2Linear OA(2237, 8207, F2, 37) (dual of [8207, 7970, 38]-code) [i]Code Embedding in Larger Space
3Linear OA(2238, 8208, F2, 37) (dual of [8208, 7970, 38]-code) [i]
4Linear OA(2239, 8209, F2, 37) (dual of [8209, 7970, 38]-code) [i]
5Linear OA(2240, 8210, F2, 37) (dual of [8210, 7970, 38]-code) [i]
6Linear OA(2235, 8205, F2, 36) (dual of [8205, 7970, 37]-code) [i]Truncation
7Linear OOA(2236, 4103, F2, 2, 37) (dual of [(4103, 2), 7970, 38]-NRT-code) [i]OOA Folding
8Linear OOA(2236, 2735, F2, 3, 37) (dual of [(2735, 3), 7969, 38]-NRT-code) [i]
9Linear OOA(2236, 2051, F2, 4, 37) (dual of [(2051, 4), 7968, 38]-NRT-code) [i]
10Linear OOA(2236, 1641, F2, 5, 37) (dual of [(1641, 5), 7969, 38]-NRT-code) [i]
11Linear OOA(2236, 1367, F2, 6, 37) (dual of [(1367, 6), 7966, 38]-NRT-code) [i]
12Linear OOA(2236, 1172, F2, 7, 37) (dual of [(1172, 7), 7968, 38]-NRT-code) [i]
13Linear OOA(2236, 1025, F2, 8, 37) (dual of [(1025, 8), 7964, 38]-NRT-code) [i]