Information on Result #715606
Linear OA(872, 522, F8, 27) (dual of [522, 450, 28]-code), using construction XX applied to C1 = C([48,73]), C2 = C([51,74]), C3 = C1 + C2 = C([51,73]), and C∩ = C1 ∩ C2 = C([48,74]) based on
- linear OA(867, 511, F8, 26) (dual of [511, 444, 27]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {48,49,…,73}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(864, 511, F8, 24) (dual of [511, 447, 25]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {51,52,…,74}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(870, 511, F8, 27) (dual of [511, 441, 28]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {48,49,…,74}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(861, 511, F8, 23) (dual of [511, 450, 24]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {51,52,…,73}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(82, 8, F8, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,8)), using
- Reed–Solomon code RS(6,8) [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 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(872, 520, F8, 2, 27) (dual of [(520, 2), 968, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(872, 520, F8, 3, 27) (dual of [(520, 3), 1488, 28]-NRT-code) | [i] | ||
| 3 | Digital (45, 72, 520)-net over F8 | [i] | ||
| 4 | Linear OOA(872, 261, F8, 2, 27) (dual of [(261, 2), 450, 28]-NRT-code) | [i] | OOA Folding | |