Information on Result #725132

Linear OA(2726, 186, F27, 14) (dual of [186, 160, 15]-code), using construction XX applied to C1 = C([181,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([181,12]) based on
  1. linear OA(2724, 182, F27, 13) (dual of [182, 158, 14]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  2. linear OA(2724, 182, F27, 13) (dual of [182, 158, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
  3. linear OA(2726, 182, F27, 14) (dual of [182, 156, 15]-code), using the BCH-code C(I) with length 182 | 272−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
  4. linear OA(2722, 182, F27, 12) (dual of [182, 160, 13]-code), using the expurgated narrow-sense BCH-code C(I) with length 182 | 272−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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(2780, 916, F27, 29) (dual of [916, 836, 30]-code) [i](u, u+v)-Construction
2Linear OA(27108, 19872, F27, 29) (dual of [19872, 19764, 30]-code) [i]
3Linear OOA(2726, 186, F27, 2, 14) (dual of [(186, 2), 346, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Digital (12, 26, 186)-net over F27 [i]
5Linear OOA(2726, 93, F27, 2, 14) (dual of [(93, 2), 160, 15]-NRT-code) [i]OOA Folding