Information on Result #702529

Linear OA(2220, 559, F2, 49) (dual of [559, 339, 50]-code), using construction XX applied to C1 = C([507,40]), C2 = C([0,44]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([507,44]) based on
  1. linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
  2. linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
  3. linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
  4. linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
  5. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
  6. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (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(2219, 558, F2, 48) (dual of [558, 339, 49]-code) [i]Truncation
2Linear OOA(2220, 279, F2, 2, 49) (dual of [(279, 2), 338, 50]-NRT-code) [i]OOA Folding
3Linear OOA(2220, 186, F2, 3, 49) (dual of [(186, 3), 338, 50]-NRT-code) [i]
4Linear OOA(2220, 139, F2, 4, 49) (dual of [(139, 4), 336, 50]-NRT-code) [i]