Information on Result #702498

Linear OA(2211, 559, F2, 47) (dual of [559, 348, 48]-code), using construction XX applied to C1 = C([507,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([507,42]) based on
  1. linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
  2. linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
  3. linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  4. 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]
  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(2210, 558, F2, 46) (dual of [558, 348, 47]-code) [i]Truncation
2Linear OOA(2211, 279, F2, 2, 47) (dual of [(279, 2), 347, 48]-NRT-code) [i]OOA Folding
3Linear OOA(2211, 186, F2, 3, 47) (dual of [(186, 3), 347, 48]-NRT-code) [i]
4Linear OOA(2211, 139, F2, 4, 47) (dual of [(139, 4), 345, 48]-NRT-code) [i]
5Linear OOA(2211, 111, F2, 5, 47) (dual of [(111, 5), 344, 48]-NRT-code) [i]