Information on Result #731339
Linear OA(932, 13132, F9, 8) (dual of [13132, 13100, 9]-code), using trace code based on linear OA(8116, 6566, F81, 8) (dual of [6566, 6550, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(5) [i] based on
- linear OA(8115, 6561, F81, 8) (dual of [6561, 6546, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(8111, 6561, F81, 6) (dual of [6561, 6550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(933, 13133, F9, 8) (dual of [13133, 13100, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(932, 13132, F9, 2, 8) (dual of [(13132, 2), 26232, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(932, 13132, F9, 3, 8) (dual of [(13132, 3), 39364, 9]-NRT-code) | [i] | ||
| 4 | Digital (24, 32, 13132)-net over F9 | [i] | ||
| 5 | Linear OOA(932, 6566, F9, 2, 8) (dual of [(6566, 2), 13100, 9]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(932, 4377, F9, 3, 8) (dual of [(4377, 3), 13099, 9]-NRT-code) | [i] | ||
| 7 | Linear OOA(932, 3283, F9, 8, 8) (dual of [(3283, 8), 26232, 9]-NRT-code) | [i] | OA Folding and Stacking | |