Information on Result #730310
Linear OA(8174, 417, F81, 40) (dual of [417, 343, 41]-code), using construction XX applied to C1 = C([20,58]), C2 = C([19,56]), C3 = C1 + C2 = C([20,56]), and C∩ = C1 ∩ C2 = C([19,58]) based on
- linear OA(8171, 410, F81, 39) (dual of [410, 339, 40]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {20,21,…,58}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(8169, 410, F81, 38) (dual of [410, 341, 39]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {19,20,…,56}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(8173, 410, F81, 40) (dual of [410, 337, 41]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {19,20,…,58}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(8167, 410, F81, 37) (dual of [410, 343, 38]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {20,21,…,56}, and designed minimum distance d ≥ |I|+1 = 38 [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(8174, 208, F81, 2, 40) (dual of [(208, 2), 342, 41]-NRT-code) | [i] | OOA Folding | |