Information on Result #691700
Linear OA(1687, 1048622, F16, 17) (dual of [1048622, 1048535, 18]-code), using construction X applied to Ce(16) ⊂ Ce(8) 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(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(1611, 46, F16, 7) (dual of [46, 35, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(1611, 51, F16, 7) (dual of [51, 40, 8]-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(1688, 1048623, F16, 17) (dual of [1048623, 1048535, 18]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(1686, 1048621, F16, 16) (dual of [1048621, 1048535, 17]-code) | [i] | Truncation | |
| 3 | Linear OOA(1687, 524311, F16, 2, 17) (dual of [(524311, 2), 1048535, 18]-NRT-code) | [i] | OOA Folding | |