Information on Result #691576
Linear OA(1661, 1048581, F16, 13) (dual of [1048581, 1048520, 14]-code), using construction X applied to Ce(12) ⊂ Ce(11) based on
- linear OA(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-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(1670, 1048619, F16, 13) (dual of [1048619, 1048549, 14]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(1671, 1048666, F16, 13) (dual of [1048666, 1048595, 14]-code) | [i] | ||
| 3 | Linear OA(1672, 1048840, F16, 13) (dual of [1048840, 1048768, 14]-code) | [i] | ||
| 4 | Linear OOA(1661, 1048581, F16, 2, 13) (dual of [(1048581, 2), 2097101, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (48, 61, 1048581)-net over F16 | [i] | ||
| 6 | Linear OOA(1661, 524290, F16, 2, 13) (dual of [(524290, 2), 1048519, 14]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(1661, 174763, F16, 13, 13) (dual of [(174763, 13), 2271858, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |