Information on Result #823149
Linear OOA(4127, 2097171, F4, 2, 15) (dual of [(2097171, 2), 4194215, 16]-NRT-code), using OOA 2-folding based on linear OA(4127, 4194342, F4, 15) (dual of [4194342, 4194215, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(4122, 4194304, F4, 15) (dual of [4194304, 4194182, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(489, 4194304, F4, 11) (dual of [4194304, 4194215, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), 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(4128, 2097171, F4, 2, 15) (dual of [(2097171, 2), 4194214, 16]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(4127, 2097171, F4, 3, 15) (dual of [(2097171, 3), 6291386, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (112, 127, 2097171)-net over F4 | [i] | ||