Information on Result #1538241
Linear OOA(4156, 4194315, F4, 3, 17) (dual of [(4194315, 3), 12582789, 18]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(4156, 4194315, F4, 2, 17) (dual of [(4194315, 2), 8388474, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(411, 14, F4, 2, 8) (dual of [(14, 2), 17, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,19P) [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- linear OOA(4145, 4194301, F4, 2, 17) (dual of [(4194301, 2), 8388457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4145, large, F4, 17) (dual of [large, large−145, 18]-code), using
- OOA 2-folding [i] based on linear OA(4145, 8388602, F4, 17) (dual of [8388602, 8388457, 18]-code), using
- linear OOA(411, 14, F4, 2, 8) (dual of [(14, 2), 17, 9]-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(4156, 1398104, F4, 21, 17) (dual of [(1398104, 21), 29360028, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |