Information on Result #667872
Linear OA(3212, 3972, F32, 5) (dual of [3972, 3960, 6]-code), using generalized (u, u+v)-construction based on
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(321, 993, F32, 1) (dual of [993, 992, 2]-code) (see above)
- linear OA(323, 993, F32, 2) (dual of [993, 990, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(323, 1023, F32, 2) (dual of [1023, 1020, 3]-code), using
- linear OA(327, 993, F32, 5) (dual of [993, 986, 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(3212, 3972, F32, 2, 5) (dual of [(3972, 2), 7932, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (7, 12, 3972)-net over F32 | [i] | ||
| 3 | Linear OOA(3212, 1986, F32, 2, 5) (dual of [(1986, 2), 3960, 6]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(3212, 1985, F32, 5, 5) (dual of [(1985, 5), 9913, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |