Information on Result #723110
Linear OA(2541, 657, F25, 16) (dual of [657, 616, 17]-code), using construction XX applied to C1 = C([3,15]), C2 = C([0,6]), C3 = C1 + C2 = C([3,6]), and C∩ = C1 ∩ C2 = C([0,15]) based on
- linear OA(2526, 624, F25, 13) (dual of [624, 598, 14]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,15}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(2531, 624, F25, 16) (dual of [624, 593, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(258, 624, F25, 4) (dual of [624, 616, 5]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,5,6}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(258, 26, F25, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,25)), using
- extended Reed–Solomon code RSe(18,25) [i]
- 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, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+5P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- linear OA(252, 7, F25, 2) (dual of [7, 5, 3]-code or 7-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
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.