Information on Result #691604
Linear OA(1657, 1048587, F16, 12) (dual of [1048587, 1048530, 13]-code), using construction X applied to Ce(11) ⊂ Ce(9) 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(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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(1665, 1048620, F16, 12) (dual of [1048620, 1048555, 13]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1657, 1048587, F16, 2, 12) (dual of [(1048587, 2), 2097117, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (45, 57, 1048587)-net over F16 | [i] | ||
| 4 | Linear OOA(1657, 524293, F16, 2, 12) (dual of [(524293, 2), 1048529, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1657, 174764, F16, 12, 12) (dual of [(174764, 12), 2097111, 13]-NRT-code) | [i] | OA Folding and Stacking | |