Information on Result #731098
Linear OA(832, 524294, F8, 6) (dual of [524294, 524262, 7]-code), using trace code based on linear OA(6416, 262147, F64, 6) (dual of [262147, 262131, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- 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(6413, 262144, F64, 5) (dual of [262144, 262131, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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(833, 524295, F8, 6) (dual of [524295, 524262, 7]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(832, 524294, F8, 2, 6) (dual of [(524294, 2), 1048556, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(832, 524294, F8, 3, 6) (dual of [(524294, 3), 1572850, 7]-NRT-code) | [i] | ||
| 4 | Digital (26, 32, 524294)-net over F8 | [i] | ||
| 5 | Linear OA(833, 524296, F8, 6) (dual of [524296, 524263, 7]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(832, 262147, F8, 2, 6) (dual of [(262147, 2), 524262, 7]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(832, 174764, F8, 3, 6) (dual of [(174764, 3), 524260, 7]-NRT-code) | [i] | ||
| 8 | Linear OOA(832, 174764, F8, 6, 6) (dual of [(174764, 6), 1048552, 7]-NRT-code) | [i] | OA Folding and Stacking | |