Information on Result #686399
Linear OA(850, 2097160, F8, 8) (dual of [2097160, 2097110, 9]-code), using construction X4 applied to C([1,8]) ⊂ C([1,6]) based on
- linear OA(849, 2097151, F8, 8) (dual of [2097151, 2097102, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(842, 2097151, F8, 6) (dual of [2097151, 2097109, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(88, 9, F8, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,8)), using
- dual of repetition code with length 9 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(81, 511, F8, 1) (dual of [511, 510, 2]-code), 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(850, 2097160, F8, 2, 8) (dual of [(2097160, 2), 4194270, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(850, 2097160, F8, 3, 8) (dual of [(2097160, 3), 6291430, 9]-NRT-code) | [i] | ||
| 3 | Digital (42, 50, 2097160)-net over F8 | [i] | ||
| 4 | Linear OOA(850, 1048580, F8, 2, 8) (dual of [(1048580, 2), 2097110, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(850, 699053, F8, 3, 8) (dual of [(699053, 3), 2097109, 9]-NRT-code) | [i] | ||
| 6 | Linear OOA(850, 524290, F8, 8, 8) (dual of [(524290, 8), 4194270, 9]-NRT-code) | [i] | OA Folding and Stacking | |