Information on Result #724845
Linear OA(25110, 663, F25, 51) (dual of [663, 553, 52]-code), using construction XX applied to C1 = C([7,51]), C2 = C([1,40]), C3 = C1 + C2 = C([7,40]), and C∩ = C1 ∩ C2 = C([1,51]) based on
- linear OA(2587, 624, F25, 45) (dual of [624, 537, 46]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,51}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2577, 624, F25, 40) (dual of [624, 547, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2595, 624, F25, 51) (dual of [624, 529, 52]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(2567, 624, F25, 34) (dual of [624, 557, 35]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,40}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2510, 26, F25, 10) (dual of [26, 16, 11]-code or 26-arc in PG(9,25)), using
- extended Reed–Solomon code RSe(16,25) [i]
- algebraic-geometric code AG(F, Q+6P) 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,5P) with degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(255, 13, F25, 5) (dual of [13, 8, 6]-code or 13-arc in PG(4,25)), using
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), using
- Reed–Solomon code RS(20,25) [i]
- discarding factors / shortening the dual code based on linear OA(255, 25, F25, 5) (dual of [25, 20, 6]-code or 25-arc in PG(4,25)), 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
None.