Information on Result #686637
Linear OA(892, 32780, F8, 21) (dual of [32780, 32688, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,9]) based on
- linear OA(891, 32769, F8, 21) (dual of [32769, 32678, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(881, 32769, F8, 19) (dual of [32769, 32688, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 810−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(81, 11, F8, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 1) (dual of [s, s−1, 2]-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 OA(893, 32781, F8, 21) (dual of [32781, 32688, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(8108, 32845, F8, 21) (dual of [32845, 32737, 22]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(892, 23946, F8, 2, 21) (dual of [(23946, 2), 47800, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(892, 23946, F8, 3, 21) (dual of [(23946, 3), 71746, 22]-NRT-code) | [i] | ||
| 5 | Digital (71, 92, 23946)-net over F8 | [i] | ||
| 6 | Linear OOA(892, 16390, F8, 2, 21) (dual of [(16390, 2), 32688, 22]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(892, 10926, F8, 3, 21) (dual of [(10926, 3), 32686, 22]-NRT-code) | [i] | ||