Information on Result #691580
Linear OA(1646, 1048581, F16, 10) (dual of [1048581, 1048535, 11]-code), using construction X applied to Ce(9) ⊂ Ce(8) based on
- 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(1641, 1048576, F16, 9) (dual of [1048576, 1048535, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(1653, 1048822, F16, 10) (dual of [1048822, 1048769, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1646, 1048581, F16, 2, 10) (dual of [(1048581, 2), 2097116, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (36, 46, 1048581)-net over F16 | [i] | ||
| 4 | Linear OOA(1646, 524290, F16, 2, 10) (dual of [(524290, 2), 1048534, 11]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(1646, 209716, F16, 10, 10) (dual of [(209716, 10), 2097114, 11]-NRT-code) | [i] | OA Folding and Stacking | |