Information on Result #664029
Linear OA(924, 116667, F9, 5) (dual of [116667, 116643, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(90, 12963, F9, 0) (dual of [12963, 12963, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(90, 12963, F9, 0) (dual of [12963, 12963, 1]-code) (see above)
- linear OA(90, 12963, F9, 0) (dual of [12963, 12963, 1]-code) (see above)
- linear OA(90, 12963, F9, 0) (dual of [12963, 12963, 1]-code) (see above)
- linear OA(91, 12963, F9, 1) (dual of [12963, 12962, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(91, 12963, F9, 1) (dual of [12963, 12962, 2]-code) (see above)
- linear OA(91, 12963, F9, 1) (dual of [12963, 12962, 2]-code) (see above)
- linear OA(96, 12963, F9, 2) (dual of [12963, 12957, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 59049, F9, 2) (dual of [59049, 59043, 3]-code), using
- an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(96, 59049, F9, 2) (dual of [59049, 59043, 3]-code), using
- linear OA(915, 12963, F9, 5) (dual of [12963, 12948, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), using
- trace code [i] based on linear OA(817, 6481, F81, 5) (dual of [6481, 6474, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(914, 12962, F9, 5) (dual of [12962, 12948, 6]-code), 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 OOA(924, 58333, F9, 2, 5) (dual of [(58333, 2), 116642, 6]-NRT-code) | [i] | OOA Folding | |