Information on Result #702026

Linear OA(2192, 282, F2, 57) (dual of [282, 90, 58]-code), using construction XX applied to C1 = C([251,50]), C2 = C([0,52]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([251,52]) based on
  1. linear OA(2181, 255, F2, 55) (dual of [255, 74, 56]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,50}, and designed minimum distance d ≥ |I|+1 = 56 [i]
  2. linear OA(2169, 255, F2, 53) (dual of [255, 86, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
  3. linear OA(2185, 255, F2, 57) (dual of [255, 70, 58]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,52}, and designed minimum distance d ≥ |I|+1 = 58 [i]
  4. linear OA(2165, 255, F2, 51) (dual of [255, 90, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
  5. linear OA(26, 22, F2, 3) (dual of [22, 16, 4]-code or 22-cap in PG(5,2)), using
  6. linear OA(21, 5, F2, 1) (dual of [5, 4, 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(2191, 281, F2, 56) (dual of [281, 90, 57]-code) [i]Truncation
2Linear OOA(2192, 141, F2, 2, 57) (dual of [(141, 2), 90, 58]-NRT-code) [i]OOA Folding
3Linear OOA(2192, 94, F2, 3, 57) (dual of [(94, 3), 90, 58]-NRT-code) [i]