Information on Result #672924

Linear OA(2240, 2112, F2, 41) (dual of [2112, 1872, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
  1. linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  3. linear OA(219, 63, F2, 7) (dual of [63, 44, 8]-code), using
    • the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 8 [i]

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(2239, 2111, F2, 40) (dual of [2111, 1872, 41]-code) [i]Truncation
2Linear OOA(2240, 1056, F2, 2, 41) (dual of [(1056, 2), 1872, 42]-NRT-code) [i]OOA Folding
3Linear OOA(2240, 704, F2, 3, 41) (dual of [(704, 3), 1872, 42]-NRT-code) [i]
4Linear OOA(2240, 528, F2, 4, 41) (dual of [(528, 4), 1872, 42]-NRT-code) [i]
5Linear OOA(2240, 422, F2, 5, 41) (dual of [(422, 5), 1870, 42]-NRT-code) [i]
6Linear OOA(2240, 352, F2, 6, 41) (dual of [(352, 6), 1872, 42]-NRT-code) [i]
7Linear OOA(2240, 301, F2, 7, 41) (dual of [(301, 7), 1867, 42]-NRT-code) [i]
8Linear OOA(2240, 264, F2, 8, 41) (dual of [(264, 8), 1872, 42]-NRT-code) [i]