Information on Result #895777
Linear OOA(4232, 4194315, F4, 2, 25) (dual of [(4194315, 2), 8388398, 26]-NRT-code), using (u, u+v)-construction based on
- linear OOA(415, 14, F4, 2, 12) (dual of [(14, 2), 13, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,15P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- linear OOA(4217, 4194301, F4, 2, 25) (dual of [(4194301, 2), 8388385, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- OOA 2-folding [i] based on linear OA(4217, 8388602, F4, 25) (dual of [8388602, 8388385, 26]-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(4232, 4194315, F4, 3, 25) (dual of [(4194315, 3), 12582713, 26]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (207, 232, 4194315)-net over F4 | [i] | ||