Information on Result #664749
Linear OA(1611, 723, F16, 5) (dual of [723, 712, 6]-code), using (u, u−v, u+v+w)-construction based on
- linear OA(161, 241, F16, 1) (dual of [241, 240, 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(163, 241, F16, 2) (dual of [241, 238, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(163, 255, F16, 2) (dual of [255, 252, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 162−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(163, 255, F16, 2) (dual of [255, 252, 3]-code), using
- linear OA(167, 241, F16, 5) (dual of [241, 234, 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(1611, 723, F16, 2, 5) (dual of [(723, 2), 1435, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (6, 11, 723)-net over F16 | [i] | ||
| 3 | Linear OOA(1611, 361, F16, 2, 5) (dual of [(361, 2), 711, 6]-NRT-code) | [i] | OOA Folding | |