Information on Result #702920

Linear OA(2203, 1061, F2, 40) (dual of [1061, 858, 41]-code), using construction XX applied to C1 = C([1019,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([1019,36]) based on
  1. 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]
  2. linear OA(2175, 1023, F2, 36) (dual of [1023, 848, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(2196, 1023, F2, 41) (dual of [1023, 827, 42]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
  5. linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-cap in PG(5,2)), using
  6. linear OA(21, 11, F2, 1) (dual of [11, 10, 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(2205, 1063, F2, 40) (dual of [1063, 858, 41]-code) [i]Code Embedding in Larger Space
2Linear OA(2204, 1062, F2, 41) (dual of [1062, 858, 42]-code) [i]Adding a Parity Check Bit
3Linear OOA(2203, 530, F2, 2, 40) (dual of [(530, 2), 857, 41]-NRT-code) [i]OOA Folding
4Linear OOA(2203, 265, F2, 4, 40) (dual of [(265, 4), 857, 41]-NRT-code) [i]
5Linear OOA(2203, 212, F2, 5, 40) (dual of [(212, 5), 857, 41]-NRT-code) [i]