Information on Result #735495
Linear OA(8122, 531526, F81, 7) (dual of [531526, 531504, 8]-code), using (u, u+v)-construction based on
- linear OA(813, 82, F81, 3) (dual of [82, 79, 4]-code or 82-arc in PG(2,81) or 82-cap in PG(2,81)), using
- extended Reed–Solomon code RSe(79,81) [i]
- oval in PG(2, 81) [i]
- linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 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
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
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(8122, 531526, F81, 2, 7) (dual of [(531526, 2), 1063030, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8122, 531526, F81, 3, 7) (dual of [(531526, 3), 1594556, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(8122, 531526, F81, 4, 7) (dual of [(531526, 4), 2126082, 8]-NRT-code) | [i] | ||
| 4 | Digital (15, 22, 531526)-net over F81 | [i] | ||
| 5 | Linear OOA(8122, 265763, F81, 2, 7) (dual of [(265763, 2), 531504, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8122, 177175, F81, 3, 7) (dual of [(177175, 3), 531503, 8]-NRT-code) | [i] | ||