Information on Result #823841
Linear OOA(4185, 2097178, F4, 2, 22) (dual of [(2097178, 2), 4194171, 23]-NRT-code), using OOA 2-folding based on linear OA(4185, 4194356, F4, 22) (dual of [4194356, 4194171, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4177, 4194304, F4, 22) (dual of [4194304, 4194127, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(48, 52, F4, 4) (dual of [52, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 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(4187, 2097179, F4, 2, 22) (dual of [(2097179, 2), 4194171, 23]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(4189, 2097180, F4, 2, 22) (dual of [(2097180, 2), 4194171, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(4186, 2097178, F4, 2, 22) (dual of [(2097178, 2), 4194170, 23]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(4185, 1662948, F4, 3, 22) (dual of [(1662948, 3), 4988659, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (163, 185, 1662948)-net over F4 | [i] | ||