Information on Result #703024

Linear OA(2248, 1076, F2, 48) (dual of [1076, 828, 49]-code), using construction XX applied to C1 = C([1019,40]), C2 = C([1,44]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([1019,44]) based on
  1. linear OA(2216, 1023, F2, 45) (dual of [1023, 807, 46]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
  2. linear OA(2215, 1023, F2, 44) (dual of [1023, 808, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
  3. linear OA(2236, 1023, F2, 49) (dual of [1023, 787, 50]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  4. linear OA(2195, 1023, F2, 40) (dual of [1023, 828, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), 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(2250, 1078, F2, 48) (dual of [1078, 828, 49]-code) [i]Code Embedding in Larger Space
2Linear OA(2249, 1077, F2, 49) (dual of [1077, 828, 50]-code) [i]Adding a Parity Check Bit
3Linear OOA(2248, 538, F2, 2, 48) (dual of [(538, 2), 828, 49]-NRT-code) [i]OOA Folding
4Linear OOA(2248, 269, F2, 4, 48) (dual of [(269, 4), 828, 49]-NRT-code) [i]
5Linear OOA(2248, 215, F2, 5, 48) (dual of [(215, 5), 827, 49]-NRT-code) [i]