Information on Result #702766

Linear OA(2118, 1061, F2, 22) (dual of [1061, 943, 23]-code), using construction XX applied to C1 = C([1019,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([1019,18]) based on
  1. linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(290, 1023, F2, 18) (dual of [1023, 933, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
  4. linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(2120, 1063, F2, 22) (dual of [1063, 943, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(2119, 1062, F2, 23) (dual of [1062, 943, 24]-code) [i]Adding a Parity Check Bit
3Linear OOA(2118, 530, F2, 2, 22) (dual of [(530, 2), 942, 23]-NRT-code) [i]OOA Folding
4Linear OOA(2118, 265, F2, 4, 22) (dual of [(265, 4), 942, 23]-NRT-code) [i]
5Linear OOA(2118, 212, F2, 5, 22) (dual of [(212, 5), 942, 23]-NRT-code) [i]