Information on Result #1302406
Linear OA(839, 524296, F8, 7) (dual of [524296, 524257, 8]-code), using construction X with Varšamov bound based on
- linear OA(838, 524294, F8, 7) (dual of [524294, 524256, 8]-code), using
- trace code [i] 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
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- trace code [i] based on linear OA(6419, 262147, F64, 7) (dual of [262147, 262128, 8]-code), using
- linear OA(838, 524295, F8, 6) (dual of [524295, 524257, 7]-code), using Gilbert–Varšamov bound and bm = 838 > Vbs−1(k−1) = 5 548501 409905 442638 665188 914287 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(839, 524296, F8, 2, 7) (dual of [(524296, 2), 1048553, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(839, 524296, F8, 3, 7) (dual of [(524296, 3), 1572849, 8]-NRT-code) | [i] | ||
| 3 | Digital (32, 39, 524296)-net over F8 | [i] | ||
| 4 | Linear OOA(839, 262148, F8, 2, 7) (dual of [(262148, 2), 524257, 8]-NRT-code) | [i] | OOA Folding | |