Information on Result #672840

Linear OA(2158, 4109, F2, 27) (dual of [4109, 3951, 28]-code), using construction X applied to Ce(26) ⊂ Ce(24) based on
  1. linear OA(2157, 4096, F2, 27) (dual of [4096, 3939, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  2. linear OA(2145, 4096, F2, 25) (dual of [4096, 3951, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  3. linear OA(21, 13, F2, 1) (dual of [13, 12, 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(2158, 4109, F2, 26) (dual of [4109, 3951, 27]-code) [i]Strength Reduction
2Linear OA(2159, 4110, F2, 27) (dual of [4110, 3951, 28]-code) [i]Code Embedding in Larger Space
3Linear OA(2160, 4111, F2, 27) (dual of [4111, 3951, 28]-code) [i]
4Linear OA(2161, 4112, F2, 27) (dual of [4112, 3951, 28]-code) [i]
5Linear OA(2162, 4113, F2, 27) (dual of [4113, 3951, 28]-code) [i]
6Linear OA(2157, 4108, F2, 26) (dual of [4108, 3951, 27]-code) [i]Truncation
7Linear OOA(2158, 2054, F2, 2, 27) (dual of [(2054, 2), 3950, 28]-NRT-code) [i]OOA Folding
8Linear OOA(2158, 1369, F2, 3, 27) (dual of [(1369, 3), 3949, 28]-NRT-code) [i]
9Linear OOA(2158, 1027, F2, 4, 27) (dual of [(1027, 4), 3950, 28]-NRT-code) [i]
10Linear OOA(2158, 821, F2, 5, 27) (dual of [(821, 5), 3947, 28]-NRT-code) [i]
11Linear OOA(2158, 684, F2, 6, 27) (dual of [(684, 6), 3946, 28]-NRT-code) [i]
12Linear OOA(2158, 587, F2, 7, 27) (dual of [(587, 7), 3951, 28]-NRT-code) [i]
13Linear OOA(2158, 513, F2, 8, 27) (dual of [(513, 8), 3946, 28]-NRT-code) [i]