Information on Result #691599
Linear OA(1692, 1048587, F16, 20) (dual of [1048587, 1048495, 21]-code), using construction X applied to Ce(19) ⊂ Ce(17) based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1681, 1048576, F16, 18) (dual of [1048576, 1048495, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [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(16108, 1048652, F16, 20) (dual of [1048652, 1048544, 21]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1692, 615925, F16, 2, 20) (dual of [(615925, 2), 1231758, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (72, 92, 615925)-net over F16 | [i] | ||
| 4 | Linear OOA(1692, 524293, F16, 2, 20) (dual of [(524293, 2), 1048494, 21]-NRT-code) | [i] | OOA Folding | |