Information on Result #823520
Linear OOA(4165, 2097184, F4, 2, 19) (dual of [(2097184, 2), 4194203, 20]-NRT-code), using OOA 2-folding based on linear OA(4165, 4194368, F4, 19) (dual of [4194368, 4194203, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(12) [i] based on
- linear OA(4155, 4194304, F4, 19) (dual of [4194304, 4194149, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(4100, 4194304, F4, 13) (dual of [4194304, 4194204, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(410, 64, F4, 5) (dual of [64, 54, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
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(4165, 2097184, F4, 3, 19) (dual of [(2097184, 3), 6291387, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (146, 165, 2097184)-net over F4 | [i] | ||