Information on Result #693395
Linear OA(2569, 15655, F25, 21) (dual of [15655, 15586, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,6]) based on
- linear OA(2561, 15626, F25, 21) (dual of [15626, 15565, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2537, 15626, F25, 13) (dual of [15626, 15589, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(258, 29, F25, 7) (dual of [29, 21, 8]-code), using
- construction X applied to AG(F,9P) ⊂ AG(F,10P) [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(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F,9P) ⊂ AG(F,10P) [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(2569, 7827, F25, 2, 21) (dual of [(7827, 2), 15585, 22]-NRT-code) | [i] | OOA Folding | |