Information on Result #823068
Linear OOA(4116, 2097171, F4, 2, 14) (dual of [(2097171, 2), 4194226, 15]-NRT-code), using OOA 2-folding based on linear OA(4116, 4194342, F4, 14) (dual of [4194342, 4194226, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(478, 4194304, F4, 10) (dual of [4194304, 4194226, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [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(4117, 2097171, F4, 2, 14) (dual of [(2097171, 2), 4194225, 15]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2232, 4194342, F2, 2, 14) (dual of [(4194342, 2), 8388452, 15]-NRT-code) | [i] | Trace Code for OOAs | |
| 3 | Linear OOA(4116, 2097171, F4, 3, 14) (dual of [(2097171, 3), 6291397, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Digital (102, 116, 2097171)-net over F4 | [i] | ||