Information on Result #679173
Linear OA(499, 16419, F4, 18) (dual of [16419, 16320, 19]-code), using construction X applied to Ce(17) ⊂ Ce(12) based on
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(464, 16384, F4, 13) (dual of [16384, 16320, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 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 OA(4100, 16420, F4, 18) (dual of [16420, 16320, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4101, 16421, F4, 18) (dual of [16421, 16320, 19]-code) | [i] | ||
| 3 | Linear OA(4102, 16422, F4, 18) (dual of [16422, 16320, 19]-code) | [i] | ||
| 4 | Linear OA(4103, 16423, F4, 18) (dual of [16423, 16320, 19]-code) | [i] | ||
| 5 | Linear OA(4104, 16424, F4, 18) (dual of [16424, 16320, 19]-code) | [i] | ||
| 6 | Linear OOA(499, 11029, F4, 2, 18) (dual of [(11029, 2), 21959, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(499, 11029, F4, 3, 18) (dual of [(11029, 3), 32988, 19]-NRT-code) | [i] | ||
| 8 | Digital (81, 99, 11029)-net over F4 | [i] | ||
| 9 | Linear OA(4101, 16422, F4, 18) (dual of [16422, 16321, 19]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4102, 16424, F4, 18) (dual of [16424, 16322, 19]-code) | [i] | ||
| 11 | Linear OA(4103, 16426, F4, 18) (dual of [16426, 16323, 19]-code) | [i] | ||
| 12 | Linear OA(4104, 16428, F4, 18) (dual of [16428, 16324, 19]-code) | [i] | ||
| 13 | Linear OOA(499, 8209, F4, 2, 18) (dual of [(8209, 2), 16319, 19]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(499, 5473, F4, 3, 18) (dual of [(5473, 3), 16320, 19]-NRT-code) | [i] | ||
| 15 | Linear OOA(499, 1824, F4, 18, 18) (dual of [(1824, 18), 32733, 19]-NRT-code) | [i] | OA Folding and Stacking | |