Information on Result #731343
Linear OA(936, 13134, F9, 9) (dual of [13134, 13098, 10]-code), using trace code based on linear OA(8118, 6567, F81, 9) (dual of [6567, 6549, 10]-code), using
- construction X applied to C([0,4]) ⊂ C([0,3]) [i] based on
- linear OA(8117, 6562, F81, 9) (dual of [6562, 6545, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 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(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(937, 13135, F9, 9) (dual of [13135, 13098, 10]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(936, 13134, F9, 2, 9) (dual of [(13134, 2), 26232, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(936, 13134, F9, 3, 9) (dual of [(13134, 3), 39366, 10]-NRT-code) | [i] | ||
| 4 | Digital (27, 36, 13134)-net over F9 | [i] | ||
| 5 | Linear OA(937, 13136, F9, 9) (dual of [13136, 13099, 10]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(936, 6567, F9, 2, 9) (dual of [(6567, 2), 13098, 10]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(936, 4378, F9, 3, 9) (dual of [(4378, 3), 13098, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(936, 3283, F9, 9, 9) (dual of [(3283, 9), 29511, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |