Information on Result #725078
Linear OA(2719, 108, F27, 11) (dual of [108, 89, 12]-code), using construction XX applied to C1 = C([103,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([103,9]) based on
- linear OA(2717, 104, F27, 10) (dual of [104, 87, 11]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2717, 104, F27, 10) (dual of [104, 87, 11]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(2719, 104, F27, 11) (dual of [104, 85, 12]-code), using the BCH-code C(I) with length 104 | 272−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2715, 104, F27, 9) (dual of [104, 89, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 104 | 272−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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(2764, 840, F27, 23) (dual of [840, 776, 24]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(2786, 19794, F27, 23) (dual of [19794, 19708, 24]-code) | [i] | ||
| 3 | Linear OA(27108, 531553, F27, 23) (dual of [531553, 531445, 24]-code) | [i] | ||
| 4 | Linear OA(2762, 840, F27, 22) (dual of [840, 778, 23]-code) | [i] | ||
| 5 | Linear OA(2783, 19794, F27, 22) (dual of [19794, 19711, 23]-code) | [i] | ||
| 6 | Linear OA(27104, 531553, F27, 22) (dual of [531553, 531449, 23]-code) | [i] | ||
| 7 | Linear OOA(2719, 108, F27, 2, 11) (dual of [(108, 2), 197, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 8 | Digital (8, 19, 108)-net over F27 | [i] | ||
| 9 | Linear OOA(2719, 54, F27, 2, 11) (dual of [(54, 2), 89, 12]-NRT-code) | [i] | OOA Folding | |