Information on Result #682627
Linear OA(5123, 15676, F5, 23) (dual of [15676, 15553, 24]-code), using construction X applied to C([0,11]) ⊂ C([0,7]) based on
- linear OA(5109, 15626, F5, 23) (dual of [15626, 15517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(573, 15626, F5, 15) (dual of [15626, 15553, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(514, 50, F5, 7) (dual of [50, 36, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- extended Reed–Solomon code RSe(19,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- algebraic-geometric code AG(F,9P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F,6P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- trace code [i] based on linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using
- discarding factors / shortening the dual code based on linear OA(514, 52, F5, 7) (dual of [52, 38, 8]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(5124, 15677, F5, 23) (dual of [15677, 15553, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5125, 15678, F5, 23) (dual of [15678, 15553, 24]-code) | [i] | ||
| 3 | Linear OA(5126, 15679, F5, 23) (dual of [15679, 15553, 24]-code) | [i] | ||
| 4 | Linear OOA(5123, 7838, F5, 2, 23) (dual of [(7838, 2), 15553, 24]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5123, 5225, F5, 3, 23) (dual of [(5225, 3), 15552, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(5123, 1425, F5, 23, 23) (dual of [(1425, 23), 32652, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |