Information on Result #727297

Linear OA(27100, 732, F27, 52) (dual of [732, 632, 53]-code), using construction XX applied to C1 = C([727,49]), C2 = C([0,50]), C3 = C1 + C2 = C([0,49]), and C∩ = C1 ∩ C2 = C([727,50]) based on
  1. linear OA(2798, 728, F27, 51) (dual of [728, 630, 52]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,49}, and designed minimum distance d ≥ |I|+1 = 52 [i]
  2. linear OA(2798, 728, F27, 51) (dual of [728, 630, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
  3. linear OA(27100, 728, F27, 52) (dual of [728, 628, 53]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,50}, and designed minimum distance d ≥ |I|+1 = 53 [i]
  4. linear OA(2796, 728, F27, 50) (dual of [728, 632, 51]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,49], and designed minimum distance d ≥ |I|+1 = 51 [i]
  5. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (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(27105, 748, F27, 52) (dual of [748, 643, 53]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(27106, 766, F27, 52) (dual of [766, 660, 53]-code) [i]
3Linear OA(27107, 800, F27, 52) (dual of [800, 693, 53]-code) [i]
4Linear OA(27108, 847, F27, 52) (dual of [847, 739, 53]-code) [i]
5Linear OOA(27100, 366, F27, 2, 52) (dual of [(366, 2), 632, 53]-NRT-code) [i]OOA Folding