Information on Result #731096
Linear OA(828, 8204, F8, 7) (dual of [8204, 8176, 8]-code), using trace code based on linear OA(6414, 4102, F64, 7) (dual of [4102, 4088, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(6413, 4097, F64, 7) (dual of [4097, 4084, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(649, 4097, F64, 5) (dual of [4097, 4088, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(641, 5, F64, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 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 OOA(828, 8204, F8, 2, 7) (dual of [(8204, 2), 16380, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(828, 8204, F8, 3, 7) (dual of [(8204, 3), 24584, 8]-NRT-code) | [i] | ||
| 3 | Digital (21, 28, 8204)-net over F8 | [i] | ||
| 4 | Linear OOA(828, 4102, F8, 2, 7) (dual of [(4102, 2), 8176, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(828, 2734, F8, 3, 7) (dual of [(2734, 3), 8174, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(828, 2734, F8, 7, 7) (dual of [(2734, 7), 19110, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |