Information on Result #1544365
Linear OOA(4235, 4194321, F4, 3, 25) (dual of [(4194321, 3), 12582728, 26]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4235, 4194321, F4, 2, 25) (dual of [(4194321, 2), 8388407, 26]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(418, 20, F4, 2, 12) (dual of [(20, 2), 22, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,27P) [i] based on function field F/F4 with g(F) = 6 and N(F) ≥ 20, 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
- linear OOA(418, 20, F4, 2, 12) (dual of [(20, 2), 22, 13]-NRT-code), using
Mode: 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(4235, 1048580, F4, 27, 25) (dual of [(1048580, 27), 28311425, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |