Information on Result #691635
Linear OA(1633, 1048593, F16, 7) (dual of [1048593, 1048560, 8]-code), using construction X applied to Ce(6) ⊂ Ce(3) based on
- linear OA(1631, 1048576, F16, 7) (dual of [1048576, 1048545, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(1616, 1048576, F16, 4) (dual of [1048576, 1048560, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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(1633, 1048593, F16, 2, 7) (dual of [(1048593, 2), 2097153, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (26, 33, 1048593)-net over F16 | [i] | ||
| 3 | Linear OOA(1633, 524296, F16, 2, 7) (dual of [(524296, 2), 1048559, 8]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(1633, 349530, F16, 7, 7) (dual of [(349530, 7), 2446677, 8]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |