Information on Result #731143
Linear OA(876, 8204, F8, 19) (dual of [8204, 8128, 20]-code), using trace code based on linear OA(6438, 4102, F64, 19) (dual of [4102, 4064, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(6437, 4097, F64, 19) (dual of [4097, 4060, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- 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(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(877, 8205, F8, 19) (dual of [8205, 8128, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(876, 8204, F8, 2, 19) (dual of [(8204, 2), 16332, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(876, 8204, F8, 3, 19) (dual of [(8204, 3), 24536, 20]-NRT-code) | [i] | ||
| 4 | Digital (57, 76, 8204)-net over F8 | [i] | ||
| 5 | Linear OA(877, 8206, F8, 19) (dual of [8206, 8129, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(876, 4102, F8, 2, 19) (dual of [(4102, 2), 8128, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(876, 2734, F8, 3, 19) (dual of [(2734, 3), 8126, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(876, 911, F8, 19, 19) (dual of [(911, 19), 17233, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |