Information on Result #691666
Linear OA(1683, 1048608, F16, 17) (dual of [1048608, 1048525, 18]-code), using construction X applied to Ce(16) ⊂ Ce(10) based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1651, 1048576, F16, 11) (dual of [1048576, 1048525, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(167, 32, F16, 5) (dual of [32, 25, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), 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(1684, 1048609, F16, 17) (dual of [1048609, 1048525, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1682, 1048607, F16, 16) (dual of [1048607, 1048525, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(1683, 1048608, F16, 2, 17) (dual of [(1048608, 2), 2097133, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (66, 83, 1048608)-net over F16 | [i] | ||
| 5 | Linear OA(1684, 1048610, F16, 17) (dual of [1048610, 1048526, 18]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(1683, 524304, F16, 2, 17) (dual of [(524304, 2), 1048525, 18]-NRT-code) | [i] | OOA Folding | |