Information on Result #895705
Linear OOA(4206, 4194311, F4, 2, 22) (dual of [(4194311, 2), 8388416, 23]-NRT-code), using (u, u+v)-construction based on
- linear OOA(413, 10, F4, 2, 11) (dual of [(10, 2), 7, 12]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,8P) [i] based on function field F/F4 with g(F) = 2 and N(F) ≥ 10, using
- linear OOA(4193, 4194301, F4, 2, 22) (dual of [(4194301, 2), 8388409, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(4193, large, F4, 22) (dual of [large, large−193, 23]-code), using
- OOA 2-folding [i] based on linear OA(4193, 8388602, F4, 22) (dual of [8388602, 8388409, 23]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(4206, 4194311, F4, 3, 22) (dual of [(4194311, 3), 12582727, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (184, 206, 4194311)-net over F4 | [i] | ||