Information on Result #731329
Linear OA(914, 13126, F9, 4) (dual of [13126, 13112, 5]-code), using trace code based on linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(817, 6561, F81, 4) (dual of [6561, 6554, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(815, 6561, F81, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(810, 2, F81, 0) (dual of [2, 2, 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(915, 13127, F9, 4) (dual of [13127, 13112, 5]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(914, 13126, F9, 2, 4) (dual of [(13126, 2), 26238, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(914, 13126, F9, 3, 4) (dual of [(13126, 3), 39364, 5]-NRT-code) | [i] | ||
| 4 | Linear OOA(914, 6563, F9, 2, 4) (dual of [(6563, 2), 13112, 5]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(914, 6563, F9, 3, 4) (dual of [(6563, 3), 19675, 5]-NRT-code) | [i] | OA Folding and Stacking | |