Information on Result #702846

Linear OA(2188, 1068, F2, 36) (dual of [1068, 880, 37]-code), using construction XX applied to C1 = C([989,1022]), C2 = C([995,2]), C3 = C1 + C2 = C([995,1022]), and C∩ = C1 ∩ C2 = C([989,2]) based on
  1. linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,−1}, and designed minimum distance d ≥ |I|+1 = 35 [i]
  2. 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 = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  4. linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [i]
  5. linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
  6. linear OA(21, 12, F2, 1) (dual of [12, 11, 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 OOA(2188, 356, F2, 3, 36) (dual of [(356, 3), 880, 37]-NRT-code) [i]OOA Folding
2Linear OOA(2188, 267, F2, 4, 36) (dual of [(267, 4), 880, 37]-NRT-code) [i]
3Linear OOA(2188, 178, F2, 6, 36) (dual of [(178, 6), 880, 37]-NRT-code) [i]