Information on Result #731134
Linear OA(868, 8204, F8, 17) (dual of [8204, 8136, 18]-code), using trace code based on linear OA(6434, 4102, F64, 17) (dual of [4102, 4068, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,7]) [i] based on
- linear OA(6433, 4097, F64, 17) (dual of [4097, 4064, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(6429, 4097, F64, 15) (dual of [4097, 4068, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (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 OA(869, 8205, F8, 17) (dual of [8205, 8136, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(868, 8204, F8, 2, 17) (dual of [(8204, 2), 16340, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(868, 8204, F8, 3, 17) (dual of [(8204, 3), 24544, 18]-NRT-code) | [i] | ||
| 4 | Digital (51, 68, 8204)-net over F8 | [i] | ||
| 5 | Linear OA(869, 8206, F8, 17) (dual of [8206, 8137, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(868, 4102, F8, 2, 17) (dual of [(4102, 2), 8136, 18]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(868, 2734, F8, 3, 17) (dual of [(2734, 3), 8134, 18]-NRT-code) | [i] | ||
| 8 | Linear OOA(868, 1025, F8, 17, 17) (dual of [(1025, 17), 17357, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |