Information on Result #672870

Linear OA(2115, 4126, F2, 19) (dual of [4126, 4011, 20]-code), using construction X applied to Ce(18) ⊂ Ce(14) based on
  1. 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]
  2. linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(2115, 4126, F2, 18) (dual of [4126, 4011, 19]-code) [i]Strength Reduction
2Linear OA(2116, 4127, F2, 19) (dual of [4127, 4011, 20]-code) [i]Code Embedding in Larger Space
3Linear OA(2117, 4128, F2, 19) (dual of [4128, 4011, 20]-code) [i]
4Linear OA(2114, 4125, F2, 18) (dual of [4125, 4011, 19]-code) [i]Truncation
5Linear OOA(2115, 2063, F2, 2, 19) (dual of [(2063, 2), 4011, 20]-NRT-code) [i]OOA Folding
6Linear OOA(2115, 1375, F2, 3, 19) (dual of [(1375, 3), 4010, 20]-NRT-code) [i]
7Linear OOA(2115, 1031, F2, 4, 19) (dual of [(1031, 4), 4009, 20]-NRT-code) [i]
8Linear OOA(2115, 825, F2, 5, 19) (dual of [(825, 5), 4010, 20]-NRT-code) [i]
9Linear OOA(2115, 687, F2, 6, 19) (dual of [(687, 6), 4007, 20]-NRT-code) [i]
10Linear OOA(2115, 589, F2, 7, 19) (dual of [(589, 7), 4008, 20]-NRT-code) [i]
11Linear OOA(2115, 515, F2, 8, 19) (dual of [(515, 8), 4005, 20]-NRT-code) [i]
12Linear OOA(2115, 458, F2, 19, 19) (dual of [(458, 19), 8587, 20]-NRT-code) [i]OOA Folding and Stacking with Additional Row