Information on Result #731089
Linear OA(820, 524294, F8, 4) (dual of [524294, 524274, 5]-code), using trace code based on linear OA(6410, 262147, F64, 4) (dual of [262147, 262137, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(6410, 262144, F64, 4) (dual of [262144, 262134, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(647, 262144, F64, 3) (dual of [262144, 262137, 4]-code or 262144-cap in PG(6,64)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [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(821, 524295, F8, 4) (dual of [524295, 524274, 5]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(820, 524294, F8, 2, 4) (dual of [(524294, 2), 1048568, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(820, 524294, F8, 3, 4) (dual of [(524294, 3), 1572862, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(820, 262147, F8, 2, 4) (dual of [(262147, 2), 524274, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(820, 262147, F8, 3, 4) (dual of [(262147, 3), 786421, 5]-NRT-code) | [i] | OA Folding and Stacking | |