Information on Result #730434
Linear OA(8180, 825, F81, 42) (dual of [825, 745, 43]-code), using construction XX applied to C1 = C([21,61]), C2 = C([20,59]), C3 = C1 + C2 = C([21,59]), and C∩ = C1 ∩ C2 = C([20,61]) based on
- linear OA(8177, 820, F81, 41) (dual of [820, 743, 42]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {21,22,…,61}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(8177, 820, F81, 40) (dual of [820, 743, 41]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {20,21,…,59}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(8179, 820, F81, 42) (dual of [820, 741, 43]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {20,21,…,61}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(8175, 820, F81, 39) (dual of [820, 745, 40]-code), using the BCH-code C(I) with length 820 | 812−1, defining interval I = {21,22,…,59}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(811, 3, F81, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- Reed–Solomon code RS(80,81) [i]
- discarding factors / shortening the dual code based on linear OA(811, 81, F81, 1) (dual of [81, 80, 2]-code), using
- linear OA(810, 2, F81, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 | OA(27107, 825, S27, 42) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8180, 412, F81, 2, 42) (dual of [(412, 2), 744, 43]-NRT-code) | [i] | OOA Folding | |