Information on Result #724853
Linear OA(25108, 657, F25, 51) (dual of [657, 549, 52]-code), using construction XX applied to C1 = C([5,51]), C2 = C([1,40]), C3 = C1 + C2 = C([5,40]), and C∩ = C1 ∩ C2 = C([1,51]) based on
- linear OA(2591, 624, F25, 47) (dual of [624, 533, 48]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {5,6,…,51}, and designed minimum distance d ≥ |I|+1 = 48 [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(2571, 624, F25, 36) (dual of [624, 553, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {5,6,…,40}, and designed minimum distance d ≥ |I|+1 = 37 [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(253, 7, F25, 3) (dual of [7, 4, 4]-code or 7-arc in PG(2,25) or 7-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
None.