Information on Result #702437

Linear OA(2174, 531, F2, 41) (dual of [531, 357, 42]-code), using construction XX applied to C1 = C([509,36]), C2 = C([0,38]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([509,38]) based on
  1. linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
  2. linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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 = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
  5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)

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(2173, 530, F2, 40) (dual of [530, 357, 41]-code) [i]Truncation
2Linear OOA(2174, 265, F2, 2, 41) (dual of [(265, 2), 356, 42]-NRT-code) [i]OOA Folding
3Linear OOA(2174, 177, F2, 3, 41) (dual of [(177, 3), 357, 42]-NRT-code) [i]
4Linear OOA(2174, 132, F2, 4, 41) (dual of [(132, 4), 354, 42]-NRT-code) [i]
5Linear OOA(2174, 106, F2, 5, 41) (dual of [(106, 5), 356, 42]-NRT-code) [i]