Information on Result #731616
Linear OA(1688, 131082, F16, 22) (dual of [131082, 130994, 23]-code), using trace code based on linear OA(25644, 65541, F256, 22) (dual of [65541, 65497, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(19) [i] based on
- linear OA(25643, 65536, F256, 22) (dual of [65536, 65493, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(25639, 65536, F256, 20) (dual of [65536, 65497, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 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 | Linear OA(1689, 131083, F16, 22) (dual of [131083, 130994, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1688, 95739, F16, 2, 22) (dual of [(95739, 2), 191390, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (66, 88, 95739)-net over F16 | [i] | ||
| 4 | Linear OOA(1688, 65541, F16, 2, 22) (dual of [(65541, 2), 130994, 23]-NRT-code) | [i] | OOA Folding | |