Information on Result #699425
Linear OA(817, 6563, F81, 4) (dual of [6563, 6556, 5]-code), using construction X applied to Ce(3) ⊂ Ce(2) 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(914, 13126, F9, 4) (dual of [13126, 13112, 5]-code) | [i] | Trace Code | |
| 2 | Linear OA(8124, 13126, F81, 9) (dual of [13126, 13102, 10]-code) | [i] | (u, u+v)-Construction | |
| 3 | Linear OA(8132, 538007, F81, 9) (dual of [538007, 537975, 10]-code) | [i] | ||
| 4 | Linear OA(8112, 531603, F81, 4) (dual of [531603, 531591, 5]-code) | [i] | Generalized (u, u+v)-Construction | |
| 5 | Linear OOA(817, 6563, F81, 2, 4) (dual of [(6563, 2), 13119, 5]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(817, 6563, F81, 3, 4) (dual of [(6563, 3), 19682, 5]-NRT-code) | [i] | ||
| 7 | Linear OOA(817, 3281, F81, 2, 4) (dual of [(3281, 2), 6555, 5]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(817, 3281, F81, 3, 4) (dual of [(3281, 3), 9836, 5]-NRT-code) | [i] | OA Folding and Stacking | |
| 9 | Linear OOA(817, 3281, F81, 4, 4) (dual of [(3281, 4), 13117, 5]-NRT-code) | [i] | ||