Information on Result #701995

Linear OA(2172, 286, F2, 49) (dual of [286, 114, 50]-code), using construction XX applied to C1 = C([251,42]), C2 = C([0,44]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([251,44]) based on
  1. linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  2. linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
  3. linear OA(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  4. linear OA(2141, 255, F2, 43) (dual of [255, 114, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [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, 9, F2, 1) (dual of [9, 8, 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(2171, 285, F2, 48) (dual of [285, 114, 49]-code) [i]Truncation
2Linear OOA(2172, 143, F2, 2, 49) (dual of [(143, 2), 114, 50]-NRT-code) [i]OOA Folding
3Linear OOA(2172, 95, F2, 3, 49) (dual of [(95, 3), 113, 50]-NRT-code) [i]