Information on Result #664555
Linear OA(1623, 2088992, F16, 5) (dual of [2088992, 2088969, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(160, 130562, F16, 0) (dual of [130562, 130562, 1]-code) (see above)
- linear OA(161, 130562, F16, 1) (dual of [130562, 130561, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(161, 130562, F16, 1) (dual of [130562, 130561, 2]-code) (see above)
- linear OA(161, 130562, F16, 1) (dual of [130562, 130561, 2]-code) (see above)
- linear OA(166, 130562, F16, 2) (dual of [130562, 130556, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 1048576, F16, 2) (dual of [1048576, 1048570, 3]-code), using
- an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(166, 1048576, F16, 2) (dual of [1048576, 1048570, 3]-code), using
- linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 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(1623, 2088992, F16, 2, 5) (dual of [(2088992, 2), 4177961, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (18, 23, 2088992)-net over F16 | [i] | ||
| 3 | Linear OOA(1623, 1044496, F16, 2, 5) (dual of [(1044496, 2), 2088969, 6]-NRT-code) | [i] | OOA Folding | |