Information on Result #731103
Linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using trace code based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(6419, 262144, F64, 7) (dual of [262144, 262125, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(6416, 262144, F64, 6) (dual of [262144, 262128, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(640, 3, F64, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-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(839, 524295, F8, 7) (dual of [524295, 524256, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(842, 524359, F8, 7) (dual of [524359, 524317, 8]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(838, 524294, F8, 2, 7) (dual of [(524294, 2), 1048550, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(838, 524294, F8, 3, 7) (dual of [(524294, 3), 1572844, 8]-NRT-code) | [i] | ||
| 5 | Digital (31, 38, 524294)-net over F8 | [i] | ||
| 6 | Linear OA(839, 524296, F8, 7) (dual of [524296, 524257, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(838, 262147, F8, 2, 7) (dual of [(262147, 2), 524256, 8]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(838, 174764, F8, 3, 7) (dual of [(174764, 3), 524254, 8]-NRT-code) | [i] | ||
| 9 | Linear OOA(838, 174764, F8, 7, 7) (dual of [(174764, 7), 1223310, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |