Information on Result #724832
Linear OA(25105, 661, F25, 49) (dual of [661, 556, 50]-code), using construction XX applied to C1 = C([615,35]), C2 = C([0,39]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([615,39]) based on
- linear OA(2586, 624, F25, 45) (dual of [624, 538, 46]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,35}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2594, 624, F25, 49) (dual of [624, 530, 50]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,39}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- extended Reed–Solomon code RSe(18,25) [i]
- algebraic-geometric code AG(F, Q+7P) with degQ = 3 and 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, Q+5P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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 OOA(25105, 330, F25, 2, 49) (dual of [(330, 2), 555, 50]-NRT-code) | [i] | OOA Folding | |