Information on Result #702381

Linear OA(2194, 573, F2, 41) (dual of [573, 379, 42]-code), using construction XX applied to C1 = C([505,28]), C2 = C([0,34]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([505,34]) based on
  1. linear OA(2154, 511, F2, 35) (dual of [511, 357, 36]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,28}, and designed minimum distance d ≥ |I|+1 = 36 [i]
  2. linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
  3. linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,34}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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(211, 29, F2, 5) (dual of [29, 18, 6]-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(2193, 572, F2, 40) (dual of [572, 379, 41]-code) [i]Truncation
2Linear OOA(2194, 286, F2, 2, 41) (dual of [(286, 2), 378, 42]-NRT-code) [i]OOA Folding
3Linear OOA(2194, 191, F2, 3, 41) (dual of [(191, 3), 379, 42]-NRT-code) [i]
4Linear OOA(2194, 143, F2, 4, 41) (dual of [(143, 4), 378, 42]-NRT-code) [i]