Information on Result #691603
Linear OA(1667, 1048587, F16, 14) (dual of [1048587, 1048520, 15]-code), using construction X applied to Ce(13) ⊂ Ce(11) based on
- linear OA(1666, 1048576, F16, 14) (dual of [1048576, 1048510, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(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 OOA(1667, 1048587, F16, 2, 14) (dual of [(1048587, 2), 2097107, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (53, 67, 1048587)-net over F16 | [i] | ||
| 3 | Linear OOA(1667, 524293, F16, 2, 14) (dual of [(524293, 2), 1048519, 15]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(1667, 149798, F16, 14, 14) (dual of [(149798, 14), 2097105, 15]-NRT-code) | [i] | OA Folding and Stacking | |