Information on Result #856675
Linear OOA(1652, 2049, F16, 2, 19) (dual of [(2049, 2), 4046, 20]-NRT-code), using OOA 2-folding based on linear OA(1652, 4098, F16, 19) (dual of [4098, 4046, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(1652, 4099, F16, 19) (dual of [4099, 4047, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(1652, 4096, F16, 19) (dual of [4096, 4044, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1649, 4096, F16, 18) (dual of [4096, 4047, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
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(1661, 2066, F16, 2, 19) (dual of [(2066, 2), 4071, 20]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(1662, 2073, F16, 2, 19) (dual of [(2073, 2), 4084, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(1663, 2082, F16, 2, 19) (dual of [(2082, 2), 4101, 20]-NRT-code) | [i] | ||
| 4 | Linear OOA(1664, 2087, F16, 2, 19) (dual of [(2087, 2), 4110, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(1665, 2094, F16, 2, 19) (dual of [(2094, 2), 4123, 20]-NRT-code) | [i] | ||
| 6 | Digital (33, 52, 2049)-net over F16 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |