Information on Result #672869

Linear OA(2139, 4126, F2, 23) (dual of [4126, 3987, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
  1. linear OA(2133, 4096, F2, 23) (dual of [4096, 3963, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  2. linear OA(2109, 4096, F2, 19) (dual of [4096, 3987, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), 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(2139, 4126, F2, 22) (dual of [4126, 3987, 23]-code) [i]Strength Reduction
2Linear OA(2140, 4127, F2, 23) (dual of [4127, 3987, 24]-code) [i]Code Embedding in Larger Space
3Linear OA(2141, 4128, F2, 23) (dual of [4128, 3987, 24]-code) [i]
4Linear OA(2142, 4129, F2, 23) (dual of [4129, 3987, 24]-code) [i]
5Linear OA(2143, 4130, F2, 23) (dual of [4130, 3987, 24]-code) [i]
6Linear OA(2138, 4125, F2, 22) (dual of [4125, 3987, 23]-code) [i]Truncation
7Linear OOA(2139, 2063, F2, 2, 23) (dual of [(2063, 2), 3987, 24]-NRT-code) [i]OOA Folding
8Linear OOA(2139, 1375, F2, 3, 23) (dual of [(1375, 3), 3986, 24]-NRT-code) [i]
9Linear OOA(2139, 1031, F2, 4, 23) (dual of [(1031, 4), 3985, 24]-NRT-code) [i]
10Linear OOA(2139, 825, F2, 5, 23) (dual of [(825, 5), 3986, 24]-NRT-code) [i]
11Linear OOA(2139, 687, F2, 6, 23) (dual of [(687, 6), 3983, 24]-NRT-code) [i]
12Linear OOA(2139, 589, F2, 7, 23) (dual of [(589, 7), 3984, 24]-NRT-code) [i]
13Linear OOA(2139, 515, F2, 8, 23) (dual of [(515, 8), 3981, 24]-NRT-code) [i]