Information on Result #672947

Linear OA(2101, 2060, F2, 19) (dual of [2060, 1959, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
  1. linear OA(2100, 2048, F2, 19) (dual of [2048, 1948, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  2. linear OA(289, 2048, F2, 17) (dual of [2048, 1959, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
  3. linear OA(21, 12, F2, 1) (dual of [12, 11, 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(2101, 2060, F2, 18) (dual of [2060, 1959, 19]-code) [i]Strength Reduction
2Linear OA(2102, 2061, F2, 19) (dual of [2061, 1959, 20]-code) [i]Code Embedding in Larger Space
3Linear OA(2103, 2062, F2, 19) (dual of [2062, 1959, 20]-code) [i]
4Linear OA(2104, 2063, F2, 19) (dual of [2063, 1959, 20]-code) [i]
5Linear OA(2105, 2064, F2, 19) (dual of [2064, 1959, 20]-code) [i]
6Linear OA(2100, 2059, F2, 18) (dual of [2059, 1959, 19]-code) [i]Truncation
7Linear OOA(2101, 1030, F2, 2, 19) (dual of [(1030, 2), 1959, 20]-NRT-code) [i]OOA Folding
8Linear OOA(2101, 686, F2, 3, 19) (dual of [(686, 3), 1957, 20]-NRT-code) [i]
9Linear OOA(2101, 515, F2, 4, 19) (dual of [(515, 4), 1959, 20]-NRT-code) [i]
10Linear OOA(2101, 412, F2, 5, 19) (dual of [(412, 5), 1959, 20]-NRT-code) [i]
11Linear OOA(2101, 343, F2, 6, 19) (dual of [(343, 6), 1957, 20]-NRT-code) [i]
12Linear OOA(2101, 294, F2, 7, 19) (dual of [(294, 7), 1957, 20]-NRT-code) [i]
13Linear OOA(2101, 257, F2, 8, 19) (dual of [(257, 8), 1955, 20]-NRT-code) [i]