Information on Result #735421
Linear OA(8150, 531526, F81, 15) (dual of [531526, 531476, 16]-code), using (u, u+v)-construction based on
- linear OA(817, 82, F81, 7) (dual of [82, 75, 8]-code or 82-arc in PG(6,81)), using
- extended Reed–Solomon code RSe(75,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(8143, 531444, F81, 15) (dual of [531444, 531401, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(13) [i] based on
- linear OA(8143, 531441, F81, 15) (dual of [531441, 531398, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(8140, 531441, F81, 14) (dual of [531441, 531401, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(14) ⊂ Ce(13) [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 | OA(2767, 531526, S27, 15) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(8150, 531526, F81, 2, 15) (dual of [(531526, 2), 1063002, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8150, 531526, F81, 3, 15) (dual of [(531526, 3), 1594528, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(8150, 531526, F81, 4, 15) (dual of [(531526, 4), 2126054, 16]-NRT-code) | [i] | ||
| 5 | Digital (35, 50, 531526)-net over F81 | [i] | ||
| 6 | Linear OOA(8150, 265763, F81, 2, 15) (dual of [(265763, 2), 531476, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8150, 177175, F81, 3, 15) (dual of [(177175, 3), 531475, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(8150, 75932, F81, 15, 15) (dual of [(75932, 15), 1138930, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |