Information on Result #691660
Linear OA(16112, 1048607, F16, 23) (dual of [1048607, 1048495, 24]-code), using construction X applied to Ce(22) ⊂ Ce(17) based on
- linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(166, 31, F16, 4) (dual of [31, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 240, F16, 4) (dual of [240, 234, 5]-code), using
- 1 times truncation [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(166, 240, F16, 4) (dual of [240, 234, 5]-code), 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(16112, 1048607, F16, 2, 23) (dual of [(1048607, 2), 2097102, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (89, 112, 1048607)-net over F16 | [i] | ||
| 3 | Linear OOA(16112, 524303, F16, 2, 23) (dual of [(524303, 2), 1048494, 24]-NRT-code) | [i] | OOA Folding | |