Information on Result #682759
Linear OA(5141, 15675, F5, 27) (dual of [15675, 15534, 28]-code), using construction X applied to Ce(26) ⊂ Ce(18) based on
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(5142, 15676, F5, 27) (dual of [15676, 15534, 28]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5143, 15677, F5, 27) (dual of [15677, 15534, 28]-code) | [i] | ||
| 3 | Linear OA(5144, 15678, F5, 27) (dual of [15678, 15534, 28]-code) | [i] | ||
| 4 | Linear OOA(5141, 7837, F5, 2, 27) (dual of [(7837, 2), 15533, 28]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5141, 5225, F5, 3, 27) (dual of [(5225, 3), 15534, 28]-NRT-code) | [i] | ||