Information on Result #731167
Linear OA(892, 8204, F8, 23) (dual of [8204, 8112, 24]-code), using trace code based on linear OA(6446, 4102, F64, 23) (dual of [4102, 4056, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(6445, 4097, F64, 23) (dual of [4097, 4052, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(6441, 4097, F64, 21) (dual of [4097, 4056, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 644−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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(893, 8205, F8, 23) (dual of [8205, 8112, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(892, 8204, F8, 2, 23) (dual of [(8204, 2), 16316, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(892, 8204, F8, 3, 23) (dual of [(8204, 3), 24520, 24]-NRT-code) | [i] | ||
| 4 | Digital (69, 92, 8204)-net over F8 | [i] | ||
| 5 | Linear OOA(892, 4102, F8, 2, 23) (dual of [(4102, 2), 8112, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(892, 2734, F8, 3, 23) (dual of [(2734, 3), 8110, 24]-NRT-code) | [i] | ||