Information on Result #735465
Linear OA(8136, 531526, F81, 11) (dual of [531526, 531490, 12]-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(8131, 531444, F81, 11) (dual of [531444, 531413, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(8131, 531441, F81, 11) (dual of [531441, 531410, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 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(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(10) ⊂ Ce(9) [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(8136, 531526, F81, 2, 11) (dual of [(531526, 2), 1063016, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8136, 531526, F81, 3, 11) (dual of [(531526, 3), 1594542, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(8136, 531526, F81, 4, 11) (dual of [(531526, 4), 2126068, 12]-NRT-code) | [i] | ||
| 4 | Digital (25, 36, 531526)-net over F81 | [i] | ||
| 5 | Linear OOA(8136, 265763, F81, 2, 11) (dual of [(265763, 2), 531490, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8136, 177175, F81, 3, 11) (dual of [(177175, 3), 531489, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(8136, 106305, F81, 11, 11) (dual of [(106305, 11), 1169319, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |