Information on Result #730237
Linear OA(8128, 417, F81, 15) (dual of [417, 389, 16]-code), using construction XX applied to C1 = C([35,48]), C2 = C([34,46]), C3 = C1 + C2 = C([35,46]), and C∩ = C1 ∩ C2 = C([34,48]) based on
- linear OA(8125, 410, F81, 14) (dual of [410, 385, 15]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,48}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8123, 410, F81, 13) (dual of [410, 387, 14]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {34,35,…,46}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(8127, 410, F81, 15) (dual of [410, 383, 16]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {34,35,…,48}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(8121, 410, F81, 12) (dual of [410, 389, 13]-code), using the BCH-code C(I) with length 410 | 812−1, defining interval I = {35,36,…,46}, and designed minimum distance d ≥ |I|+1 = 13 [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(8128, 208, F81, 2, 15) (dual of [(208, 2), 388, 16]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(8128, 139, F81, 3, 15) (dual of [(139, 3), 389, 16]-NRT-code) | [i] | ||