Information on Result #691662
Linear OA(16103, 1048608, F16, 21) (dual of [1048608, 1048505, 22]-code), using construction X applied to Ce(20) ⊂ Ce(14) based on
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(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(16104, 1048609, F16, 21) (dual of [1048609, 1048505, 22]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(16103, 1048608, F16, 2, 21) (dual of [(1048608, 2), 2097113, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (82, 103, 1048608)-net over F16 | [i] | ||
| 4 | Linear OA(16104, 1048610, F16, 21) (dual of [1048610, 1048506, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(16103, 524304, F16, 2, 21) (dual of [(524304, 2), 1048505, 22]-NRT-code) | [i] | OOA Folding | |