Information on Result #691630
Linear OA(1658, 1048593, F16, 12) (dual of [1048593, 1048535, 13]-code), using construction X applied to Ce(11) ⊂ Ce(8) based on
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(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(1659, 1048594, F16, 12) (dual of [1048594, 1048535, 13]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(1658, 1048593, F16, 2, 12) (dual of [(1048593, 2), 2097128, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (46, 58, 1048593)-net over F16 | [i] | ||
| 4 | Linear OA(1659, 1048595, F16, 12) (dual of [1048595, 1048536, 13]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(1658, 524296, F16, 2, 12) (dual of [(524296, 2), 1048534, 13]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(1658, 174765, F16, 12, 12) (dual of [(174765, 12), 2097122, 13]-NRT-code) | [i] | OA Folding and Stacking | |