Information on Result #691798
Linear OA(1682, 65545, F16, 22) (dual of [65545, 65463, 23]-code), using construction X applied to Ce(21) ⊂ Ce(19) based on
- linear OA(1681, 65536, F16, 22) (dual of [65536, 65455, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1673, 65536, F16, 20) (dual of [65536, 65463, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(161, 9, F16, 1) (dual of [9, 8, 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
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 | OA(8110, 65545, S8, 22) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(1682, 41667, F16, 2, 22) (dual of [(41667, 2), 83252, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (60, 82, 41667)-net over F16 | [i] | ||
| 4 | Linear OOA(1682, 32772, F16, 2, 22) (dual of [(32772, 2), 65462, 23]-NRT-code) | [i] | OOA Folding | |