Information on Result #731119
Linear OA(856, 524294, F8, 10) (dual of [524294, 524238, 11]-code), using trace code based on linear OA(6428, 262147, F64, 10) (dual of [262147, 262119, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- linear OA(6428, 262144, F64, 10) (dual of [262144, 262116, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(6425, 262144, F64, 9) (dual of [262144, 262119, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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 OOA(856, 524294, F8, 2, 10) (dual of [(524294, 2), 1048532, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(856, 524294, F8, 3, 10) (dual of [(524294, 3), 1572826, 11]-NRT-code) | [i] | ||
| 3 | Digital (46, 56, 524294)-net over F8 | [i] | ||
| 4 | Linear OOA(856, 262147, F8, 2, 10) (dual of [(262147, 2), 524238, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(856, 174764, F8, 3, 10) (dual of [(174764, 3), 524236, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(856, 104858, F8, 10, 10) (dual of [(104858, 10), 1048524, 11]-NRT-code) | [i] | OA Folding and Stacking | |