Information on Result #731243
Linear OA(8136, 524304, F8, 23) (dual of [524304, 524168, 24]-code), using trace code based on linear OA(6468, 262152, F64, 23) (dual of [262152, 262084, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(6467, 262145, F64, 23) (dual of [262145, 262078, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(6461, 262145, F64, 21) (dual of [262145, 262084, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 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(8137, 524305, F8, 23) (dual of [524305, 524168, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8136, 524304, F8, 2, 23) (dual of [(524304, 2), 1048472, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8136, 524304, F8, 3, 23) (dual of [(524304, 3), 1572776, 24]-NRT-code) | [i] | ||
| 4 | Digital (113, 136, 524304)-net over F8 | [i] | ||
| 5 | Linear OOA(8136, 262152, F8, 2, 23) (dual of [(262152, 2), 524168, 24]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8136, 174768, F8, 3, 23) (dual of [(174768, 3), 524168, 24]-NRT-code) | [i] | ||