Information on Result #691626
Linear OA(1673, 1048593, F16, 15) (dual of [1048593, 1048520, 16]-code), using construction X applied to Ce(14) ⊂ Ce(11) based on
- 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(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(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 OOA(1673, 1048593, F16, 2, 15) (dual of [(1048593, 2), 2097113, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (58, 73, 1048593)-net over F16 | [i] | ||
| 3 | Linear OOA(1673, 524296, F16, 2, 15) (dual of [(524296, 2), 1048519, 16]-NRT-code) | [i] | OOA Folding | |