Information on Result #686248
Linear OA(836, 2097159, F8, 6) (dual of [2097159, 2097123, 7]-code), using construction X applied to Ce(5) ⊂ Ce(4) based on
- linear OA(836, 2097152, F8, 6) (dual of [2097152, 2097116, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(829, 2097152, F8, 5) (dual of [2097152, 2097123, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(80, 7, F8, 0) (dual of [7, 7, 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: 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(840, 2097224, F8, 6) (dual of [2097224, 2097184, 7]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(836, 2097159, F8, 2, 6) (dual of [(2097159, 2), 4194282, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(836, 2097159, F8, 3, 6) (dual of [(2097159, 3), 6291441, 7]-NRT-code) | [i] | ||
| 4 | Digital (30, 36, 2097159)-net over F8 | [i] | ||
| 5 | Linear OOA(836, 1048579, F8, 2, 6) (dual of [(1048579, 2), 2097122, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(836, 699053, F8, 3, 6) (dual of [(699053, 3), 2097123, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(836, 699053, F8, 6, 6) (dual of [(699053, 6), 4194282, 7]-NRT-code) | [i] | OA Folding and Stacking | |