Information on Result #724263
Linear OA(2597, 681, F25, 40) (dual of [681, 584, 41]-code), using construction XX applied to C1 = C([620,26]), C2 = C([8,35]), C3 = C1 + C2 = C([8,26]), and C∩ = C1 ∩ C2 = C([620,35]) based on
- linear OA(2558, 624, F25, 31) (dual of [624, 566, 32]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−4,−3,…,26}, 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 = {8,9,…,35}, 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 = {−4,−3,…,35}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2537, 624, F25, 19) (dual of [624, 587, 20]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {8,9,…,26}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2513, 31, F25, 11) (dual of [31, 18, 12]-code), using
- construction X applied to AG(F, Q+4P) ⊂ AG(F, Q+5P) [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(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using 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 (see above)
- linear OA(252, 5, F25, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,25)), using
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- Reed–Solomon code RS(23,25) [i]
- discarding factors / shortening the dual code based on linear OA(252, 25, F25, 2) (dual of [25, 23, 3]-code or 25-arc in PG(1,25)), using
- construction X applied to AG(F, Q+4P) ⊂ AG(F, Q+5P) [i] based on
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)) (see above)
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.