Information on Result #693382
Linear OA(2582, 15657, F25, 25) (dual of [15657, 15575, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,8]) based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2549, 15626, F25, 17) (dual of [15626, 15577, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(259, 31, F25, 7) (dual of [31, 22, 8]-code), using
- construction X applied to AG(F,6P) ⊂ AG(F,7P) [i] based on
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using 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]
- linear OA(254, 26, F25, 4) (dual of [26, 22, 5]-code or 26-arc in PG(3,25)), using algebraic-geometric code AG(F, Q+9P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to AG(F,6P) ⊂ AG(F,7P) [i] based on
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 OOA(2582, 7828, F25, 2, 25) (dual of [(7828, 2), 15574, 26]-NRT-code) | [i] | OOA Folding | |