Information on Result #724254
Linear OA(2596, 678, F25, 40) (dual of [678, 582, 41]-code), using construction XX applied to C1 = C([619,25]), C2 = C([7,34]), C3 = C1 + C2 = C([7,25]), and C∩ = C1 ∩ C2 = C([619,34]) based on
- linear OA(2559, 624, F25, 31) (dual of [624, 565, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,25}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2555, 624, F25, 28) (dual of [624, 569, 29]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,34}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−5,−4,…,34}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2538, 624, F25, 19) (dual of [624, 586, 20]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {7,8,…,25}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2512, 29, F25, 11) (dual of [29, 17, 12]-code), using
- construction X applied to AG(F,7P) ⊂ AG(F,8P) [i] based on
- linear OA(2511, 26, F25, 11) (dual of [26, 15, 12]-code or 26-arc in PG(10,25)), using algebraic-geometric code AG(F,7P) 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(259, 26, F25, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,25)), using algebraic-geometric code AG(F,8P) 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,7P) ⊂ AG(F,8P) [i] based on
- linear OA(258, 25, F25, 8) (dual of [25, 17, 9]-code or 25-arc in PG(7,25)), using
- Reed–Solomon code RS(17,25) [i]
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.