Information on Result #730363
Linear OA(8168, 663, F81, 36) (dual of [663, 595, 37]-code), using construction XX applied to C1 = C([25,59]), C2 = C([24,57]), C3 = C1 + C2 = C([25,57]), and C∩ = C1 ∩ C2 = C([24,59]) based on
- linear OA(8165, 656, F81, 35) (dual of [656, 591, 36]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {25,26,…,59}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(8163, 656, F81, 34) (dual of [656, 593, 35]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {24,25,…,57}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(8167, 656, F81, 36) (dual of [656, 589, 37]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {24,25,…,59}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8161, 656, F81, 33) (dual of [656, 595, 34]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {25,26,…,57}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 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 | Linear OOA(8168, 331, F81, 2, 36) (dual of [(331, 2), 594, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8168, 221, F81, 3, 36) (dual of [(221, 3), 595, 37]-NRT-code) | [i] | ||