Information on Result #724826
Linear OA(25110, 667, F25, 50) (dual of [667, 557, 51]-code), using construction XX applied to C1 = C([614,33]), C2 = C([0,39]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([614,39]) based on
- linear OA(2584, 624, F25, 44) (dual of [624, 540, 45]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−10,−9,…,33}, and designed minimum distance d ≥ |I|+1 = 45 [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(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 = {−10,−9,…,39}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2564, 624, F25, 34) (dual of [624, 560, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(259, 26, F25, 9) (dual of [26, 17, 10]-code or 26-arc in PG(8,25)), using
- extended Reed–Solomon code RSe(17,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 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, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+4P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(255, 17, F25, 5) (dual of [17, 12, 6]-code or 17-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.