Information on Result #672827

Linear OA(2260, 4161, F2, 41) (dual of [4161, 3901, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,16]) based on
  1. linear OA(2241, 4097, F2, 41) (dual of [4097, 3856, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
  2. linear OA(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
  3. linear OA(219, 64, F2, 7) (dual of [64, 45, 8]-code), using
    • an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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 OOA(2260, 1387, F2, 3, 41) (dual of [(1387, 3), 3901, 42]-NRT-code) [i]OOA Folding
2Linear OOA(2260, 1040, F2, 4, 41) (dual of [(1040, 4), 3900, 42]-NRT-code) [i]
3Linear OOA(2260, 832, F2, 5, 41) (dual of [(832, 5), 3900, 42]-NRT-code) [i]
4Linear OOA(2260, 693, F2, 6, 41) (dual of [(693, 6), 3898, 42]-NRT-code) [i]
5Linear OOA(2260, 594, F2, 7, 41) (dual of [(594, 7), 3898, 42]-NRT-code) [i]
6Linear OOA(2260, 520, F2, 8, 41) (dual of [(520, 8), 3900, 42]-NRT-code) [i]