Information on Result #731336
Linear OA(928, 13134, F9, 7) (dual of [13134, 13106, 8]-code), using trace code based on linear OA(8114, 6567, F81, 7) (dual of [6567, 6553, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([0,2]) [i] based on
- linear OA(8113, 6562, F81, 7) (dual of [6562, 6549, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(819, 6562, F81, 5) (dual of [6562, 6553, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-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 OOA(928, 13134, F9, 2, 7) (dual of [(13134, 2), 26240, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(928, 13134, F9, 3, 7) (dual of [(13134, 3), 39374, 8]-NRT-code) | [i] | ||
| 3 | Digital (21, 28, 13134)-net over F9 | [i] | ||
| 4 | Linear OOA(928, 6567, F9, 2, 7) (dual of [(6567, 2), 13106, 8]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(928, 4378, F9, 3, 7) (dual of [(4378, 3), 13106, 8]-NRT-code) | [i] | ||
| 6 | Linear OOA(928, 4377, F9, 7, 7) (dual of [(4377, 7), 30611, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |