Information on Result #703047

Linear OA(2258, 1075, F2, 51) (dual of [1075, 817, 52]-code), using construction XX applied to C1 = C([1019,42]), C2 = C([0,46]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([1019,46]) based on
  1. linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
  2. linear OA(2226, 1023, F2, 47) (dual of [1023, 797, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [i]
  3. linear OA(2246, 1023, F2, 51) (dual of [1023, 777, 52]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,46}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  4. linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
  5. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
  6. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-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(2257, 1074, F2, 50) (dual of [1074, 817, 51]-code) [i]Truncation
2Linear OOA(2258, 537, F2, 2, 51) (dual of [(537, 2), 816, 52]-NRT-code) [i]OOA Folding
3Linear OOA(2258, 358, F2, 3, 51) (dual of [(358, 3), 816, 52]-NRT-code) [i]
4Linear OOA(2258, 268, F2, 4, 51) (dual of [(268, 4), 814, 52]-NRT-code) [i]
5Linear OOA(2258, 215, F2, 5, 51) (dual of [(215, 5), 817, 52]-NRT-code) [i]
6Linear OOA(2258, 179, F2, 6, 51) (dual of [(179, 6), 816, 52]-NRT-code) [i]
7Linear OOA(2258, 153, F2, 7, 51) (dual of [(153, 7), 813, 52]-NRT-code) [i]