Information on Result #691801
Linear OA(1670, 65545, F16, 19) (dual of [65545, 65475, 20]-code), using construction X applied to Ce(18) ⊂ Ce(16) based on
- linear OA(1669, 65536, F16, 19) (dual of [65536, 65467, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(1661, 65536, F16, 17) (dual of [65536, 65475, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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 | Linear OA(1671, 65546, F16, 19) (dual of [65546, 65475, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | OA(894, 65545, S8, 19) | [i] | Discarding Parts of the Base for OAs | |
| 3 | Linear OOA(1670, 36903, F16, 2, 19) (dual of [(36903, 2), 73736, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (51, 70, 36903)-net over F16 | [i] | ||
| 5 | Linear OOA(1670, 32772, F16, 2, 19) (dual of [(32772, 2), 65474, 20]-NRT-code) | [i] | OOA Folding | |