Information on Result #724880
Linear OA(25104, 652, F25, 50) (dual of [652, 548, 51]-code), using construction XX applied to C1 = C([615,39]), C2 = C([0,40]), C3 = C1 + C2 = C([0,39]), and C∩ = C1 ∩ C2 = C([615,40]) based on
- 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(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2596, 624, F25, 50) (dual of [624, 528, 51]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−9,−8,…,40}, and designed minimum distance d ≥ |I|+1 = 51 [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(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(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, 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(25104, 326, F25, 2, 50) (dual of [(326, 2), 548, 51]-NRT-code) | [i] | OOA Folding | |