Information on Result #691571
Linear OA(1677, 1048582, F16, 17) (dual of [1048582, 1048505, 18]-code), using construction X applied to Ce(16) ⊂ Ce(14) 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(1671, 1048576, F16, 15) (dual of [1048576, 1048505, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(161, 6, F16, 1) (dual of [6, 5, 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(1676, 1048581, F16, 16) (dual of [1048581, 1048505, 17]-code) | [i] | Truncation | |
| 2 | Linear OOA(1677, 540187, F16, 2, 17) (dual of [(540187, 2), 1080297, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (60, 77, 540187)-net over F16 | [i] | ||
| 4 | Linear OOA(1677, 524291, F16, 2, 17) (dual of [(524291, 2), 1048505, 18]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1677, 131072, F16, 17, 17) (dual of [(131072, 17), 2228147, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |