Information on Result #731593
Linear OA(1672, 131082, F16, 18) (dual of [131082, 131010, 19]-code), using trace code based on linear OA(25636, 65541, F256, 18) (dual of [65541, 65505, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- linear OA(25635, 65536, F256, 18) (dual of [65536, 65501, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [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(1673, 131083, F16, 18) (dual of [131083, 131010, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1672, 99930, F16, 2, 18) (dual of [(99930, 2), 199788, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (54, 72, 99930)-net over F16 | [i] | ||
| 4 | Linear OOA(1672, 65541, F16, 2, 18) (dual of [(65541, 2), 131010, 19]-NRT-code) | [i] | OOA Folding | |