Information on Result #731105
Linear OA(840, 524306, F8, 7) (dual of [524306, 524266, 8]-code), using trace code based on linear OA(6420, 262153, F64, 7) (dual of [262153, 262133, 8]-code), using
- construction X4 applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(6419, 262145, F64, 7) (dual of [262145, 262126, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(6413, 262145, F64, 5) (dual of [262145, 262132, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(647, 8, F64, 7) (dual of [8, 1, 8]-code or 8-arc in PG(6,64)), using
- dual of repetition code with length 8 [i]
- linear OA(641, 8, F64, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), using
- Reed–Solomon code RS(63,64) [i]
- discarding factors / shortening the dual code based on linear OA(641, 64, F64, 1) (dual of [64, 63, 2]-code), 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(841, 524307, F8, 7) (dual of [524307, 524266, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(840, 524306, F8, 2, 7) (dual of [(524306, 2), 1048572, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(840, 524306, F8, 3, 7) (dual of [(524306, 3), 1572878, 8]-NRT-code) | [i] | ||
| 4 | Digital (33, 40, 524306)-net over F8 | [i] | ||
| 5 | Linear OOA(840, 262153, F8, 2, 7) (dual of [(262153, 2), 524266, 8]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(840, 174768, F8, 3, 7) (dual of [(174768, 3), 524264, 8]-NRT-code) | [i] | ||
| 7 | Linear OOA(840, 174768, F8, 7, 7) (dual of [(174768, 7), 1223336, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |