Information on Result #691634
Linear OA(1638, 1048593, F16, 8) (dual of [1048593, 1048555, 9]-code), using construction X applied to Ce(7) ⊂ Ce(4) based on
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(1621, 1048576, F16, 5) (dual of [1048576, 1048555, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(162, 17, F16, 2) (dual of [17, 15, 3]-code or 17-arc in PG(1,16)), using
- extended Reed–Solomon code RSe(15,16) [i]
- Hamming code H(2,16) [i]
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(1639, 1048594, F16, 8) (dual of [1048594, 1048555, 9]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1638, 1048593, F16, 2, 8) (dual of [(1048593, 2), 2097148, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (30, 38, 1048593)-net over F16 | [i] | ||
| 4 | Linear OOA(1638, 524296, F16, 2, 8) (dual of [(524296, 2), 1048554, 9]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1638, 262148, F16, 8, 8) (dual of [(262148, 8), 2097146, 9]-NRT-code) | [i] | OA Folding and Stacking | |