Information on Result #731392
Linear OA(976, 13134, F9, 19) (dual of [13134, 13058, 20]-code), using trace code based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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 OA(977, 13135, F9, 19) (dual of [13135, 13058, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(976, 13134, F9, 2, 19) (dual of [(13134, 2), 26192, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(976, 13134, F9, 3, 19) (dual of [(13134, 3), 39326, 20]-NRT-code) | [i] | ||
| 4 | Digital (57, 76, 13134)-net over F9 | [i] | ||
| 5 | Linear OA(977, 13136, F9, 19) (dual of [13136, 13059, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(976, 6567, F9, 2, 19) (dual of [(6567, 2), 13058, 20]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(976, 4378, F9, 3, 19) (dual of [(4378, 3), 13058, 20]-NRT-code) | [i] | ||
| 8 | Linear OOA(976, 1459, F9, 19, 19) (dual of [(1459, 19), 27645, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |