Information on Result #702827

Linear OA(2168, 1061, F2, 32) (dual of [1061, 893, 33]-code), using construction XX applied to C1 = C([1019,26]), C2 = C([1,28]), C3 = C1 + C2 = C([1,26]), and C∩ = C1 ∩ C2 = C([1019,28]) based on
  1. linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  2. linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
  3. linear OA(2161, 1023, F2, 33) (dual of [1023, 862, 34]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,28}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  4. linear OA(2130, 1023, F2, 26) (dual of [1023, 893, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(2170, 1063, F2, 32) (dual of [1063, 893, 33]-code) [i]Code Embedding in Larger Space
2Linear OA(2169, 1062, F2, 33) (dual of [1062, 893, 34]-code) [i]Adding a Parity Check Bit
3Linear OOA(2168, 530, F2, 2, 32) (dual of [(530, 2), 892, 33]-NRT-code) [i]OOA Folding
4Linear OOA(2168, 265, F2, 4, 32) (dual of [(265, 4), 892, 33]-NRT-code) [i]
5Linear OOA(2168, 212, F2, 5, 32) (dual of [(212, 5), 892, 33]-NRT-code) [i]