Information on Result #679169
Linear OA(4120, 16419, F4, 22) (dual of [16419, 16299, 23]-code), using construction X applied to Ce(21) ⊂ Ce(16) based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(4121, 16420, F4, 22) (dual of [16420, 16299, 23]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(4122, 16421, F4, 22) (dual of [16421, 16299, 23]-code) | [i] | ||
| 3 | Linear OA(4123, 16422, F4, 22) (dual of [16422, 16299, 23]-code) | [i] | ||
| 4 | Linear OA(4124, 16423, F4, 22) (dual of [16423, 16299, 23]-code) | [i] | ||
| 5 | Linear OA(4125, 16424, F4, 22) (dual of [16424, 16299, 23]-code) | [i] | ||
| 6 | Linear OOA(4120, 10563, F4, 2, 22) (dual of [(10563, 2), 21006, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 7 | Linear OOA(4120, 10563, F4, 3, 22) (dual of [(10563, 3), 31569, 23]-NRT-code) | [i] | ||
| 8 | Digital (98, 120, 10563)-net over F4 | [i] | ||
| 9 | Linear OA(4122, 16422, F4, 22) (dual of [16422, 16300, 23]-code) | [i] | Construction X with Varšamov Bound | |
| 10 | Linear OA(4123, 16424, F4, 22) (dual of [16424, 16301, 23]-code) | [i] | ||
| 11 | Linear OA(4124, 16426, F4, 22) (dual of [16426, 16302, 23]-code) | [i] | ||
| 12 | Linear OA(4125, 16428, F4, 22) (dual of [16428, 16303, 23]-code) | [i] | ||
| 13 | Linear OOA(4120, 8209, F4, 2, 22) (dual of [(8209, 2), 16298, 23]-NRT-code) | [i] | OOA Folding | |
| 14 | Linear OOA(4120, 5473, F4, 3, 22) (dual of [(5473, 3), 16299, 23]-NRT-code) | [i] | ||