Information on Result #702895

Linear OA(2193, 1055, F2, 39) (dual of [1055, 862, 40]-code), using construction XX applied to C1 = C([1019,32]), C2 = C([0,34]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1019,34]) based on
  1. linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(2166, 1023, F2, 35) (dual of [1023, 857, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
  3. linear OA(2186, 1023, F2, 39) (dual of [1023, 837, 40]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
  4. linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
  5. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
  6. linear OA(21, 6, F2, 1) (dual of [6, 5, 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(2192, 1054, F2, 38) (dual of [1054, 862, 39]-code) [i]Truncation
2Linear OOA(2193, 527, F2, 2, 39) (dual of [(527, 2), 861, 40]-NRT-code) [i]OOA Folding
3Linear OOA(2193, 351, F2, 3, 39) (dual of [(351, 3), 860, 40]-NRT-code) [i]
4Linear OOA(2193, 263, F2, 4, 39) (dual of [(263, 4), 859, 40]-NRT-code) [i]
5Linear OOA(2193, 211, F2, 5, 39) (dual of [(211, 5), 862, 40]-NRT-code) [i]