Information on Result #730372
Linear OA(8172, 663, F81, 38) (dual of [663, 591, 39]-code), using construction XX applied to C1 = C([23,59]), C2 = C([22,57]), C3 = C1 + C2 = C([23,57]), and C∩ = C1 ∩ C2 = C([22,59]) based on
- linear OA(8169, 656, F81, 37) (dual of [656, 587, 38]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {23,24,…,59}, and designed minimum distance d ≥ |I|+1 = 38 [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 = {22,23,…,57}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(8171, 656, F81, 38) (dual of [656, 585, 39]-code), using the BCH-code C(I) with length 656 | 812−1, defining interval I = {22,23,…,59}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- 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 = {23,24,…,57}, and designed minimum distance d ≥ |I|+1 = 36 [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(8172, 331, F81, 2, 38) (dual of [(331, 2), 590, 39]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8172, 221, F81, 3, 38) (dual of [(221, 3), 591, 39]-NRT-code) | [i] | ||