Information on Result #735474
Linear OA(8133, 531526, F81, 10) (dual of [531526, 531493, 11]-code), using (u, u+v)-construction based on
- linear OA(815, 82, F81, 5) (dual of [82, 77, 6]-code or 82-arc in PG(4,81)), using
- extended Reed–Solomon code RSe(77,81) [i]
- the expurgated narrow-sense BCH-code C(I) with length 82 | 812−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(8128, 531444, F81, 10) (dual of [531444, 531416, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(8128, 531441, F81, 10) (dual of [531441, 531413, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(8125, 531441, F81, 9) (dual of [531441, 531416, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [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(8133, 531526, F81, 2, 10) (dual of [(531526, 2), 1063019, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8133, 531526, F81, 3, 10) (dual of [(531526, 3), 1594545, 11]-NRT-code) | [i] | ||
| 3 | Linear OOA(8133, 531526, F81, 4, 10) (dual of [(531526, 4), 2126071, 11]-NRT-code) | [i] | ||
| 4 | Digital (23, 33, 531526)-net over F81 | [i] | ||
| 5 | Linear OOA(8133, 265763, F81, 2, 10) (dual of [(265763, 2), 531493, 11]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8133, 177175, F81, 3, 10) (dual of [(177175, 3), 531492, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(8133, 106305, F81, 10, 10) (dual of [(106305, 10), 1063017, 11]-NRT-code) | [i] | OA Folding and Stacking | |