Information on Result #725073
Linear OA(2712, 108, F27, 7) (dual of [108, 96, 8]-code), using construction XX applied to C1 = C([103,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([103,5]) based on
- linear OA(2710, 104, F27, 6) (dual of [104, 94, 7]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2710, 104, F27, 6) (dual of [104, 94, 7]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2712, 104, F27, 7) (dual of [104, 92, 8]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(278, 104, F27, 5) (dual of [104, 96, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(2741, 840, F27, 15) (dual of [840, 799, 16]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2755, 19794, F27, 15) (dual of [19794, 19739, 16]-code) | [i] | ||
| 3 | Linear OA(2769, 531553, F27, 15) (dual of [531553, 531484, 16]-code) | [i] | ||
| 4 | Linear OA(2752, 19794, F27, 14) (dual of [19794, 19742, 15]-code) | [i] | ||
| 5 | Linear OA(2765, 531553, F27, 14) (dual of [531553, 531488, 15]-code) | [i] | ||
| 6 | Linear OOA(2712, 108, F27, 2, 7) (dual of [(108, 2), 204, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Digital (5, 12, 108)-net over F27 | [i] | ||
| 8 | Linear OOA(2712, 54, F27, 2, 7) (dual of [(54, 2), 96, 8]-NRT-code) | [i] | OOA Folding | |