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
- 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]
- 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]
- 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]
- 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]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- 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:
Result | This result only | Method | ||
---|---|---|---|---|
1 | Linear OA(2780, 916, F27, 29) (dual of [916, 836, 30]-code) | [i] | (u, u+v)-Construction | |
2 | Linear OA(27108, 19872, F27, 29) (dual of [19872, 19764, 30]-code) | [i] | ||
3 | Linear OOA(2726, 186, F27, 2, 14) (dual of [(186, 2), 346, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
4 | Digital (12, 26, 186)-net over F27 | [i] | ||
5 | Linear OOA(2726, 93, F27, 2, 14) (dual of [(93, 2), 160, 15]-NRT-code) | [i] | OOA Folding |