Information on Result #731344
Linear OA(938, 1062888, F9, 7) (dual of [1062888, 1062850, 8]-code), using trace code based on linear OA(8119, 531444, F81, 7) (dual of [531444, 531425, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(8119, 531441, F81, 7) (dual of [531441, 531422, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(8116, 531441, F81, 6) (dual of [531441, 531425, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 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(939, 1062889, F9, 7) (dual of [1062889, 1062850, 8]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(942, 1062970, F9, 7) (dual of [1062970, 1062928, 8]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OOA(938, 1062888, F9, 2, 7) (dual of [(1062888, 2), 2125738, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(938, 1062888, F9, 3, 7) (dual of [(1062888, 3), 3188626, 8]-NRT-code) | [i] | ||
| 5 | Digital (31, 38, 1062888)-net over F9 | [i] | ||
| 6 | Linear OA(939, 1062890, F9, 7) (dual of [1062890, 1062851, 8]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OOA(938, 531444, F9, 2, 7) (dual of [(531444, 2), 1062850, 8]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(938, 354296, F9, 3, 7) (dual of [(354296, 3), 1062850, 8]-NRT-code) | [i] | ||
| 9 | Linear OOA(938, 354295, F9, 7, 7) (dual of [(354295, 7), 2480027, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |