Information on Result #1082646
Linear OOA(8178, 2097332, F81, 4, 17) (dual of [(2097332, 4), 8389250, 18]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8113, 182, F81, 4, 8) (dual of [(182, 4), 715, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(4;324,81) [i]
- linear OOA(819, 100, F81, 4, 8) (dual of [(100, 4), 391, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(4;F,391P) [i] based on function field F/F81 with g(F) = 1 and N(F) ≥ 100, using
- linear OOA(814, 82, F81, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(8165, 2097150, F81, 4, 17) (dual of [(2097150, 4), 8388535, 18]-NRT-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, 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(8165, large, F81, 17) (dual of [large, large−65, 18]-code), using
- OOA 4-folding [i] based on linear OA(8165, 8388600, F81, 17) (dual of [8388600, 8388535, 18]-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(8178, 1048665, F81, 20, 17) (dual of [(1048665, 20), 20973222, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |