Information on Result #723446
Linear OA(2557, 657, F25, 24) (dual of [657, 600, 25]-code), using construction XX applied to C1 = C([3,23]), C2 = C([0,14]), C3 = C1 + C2 = C([3,14]), and C∩ = C1 ∩ C2 = C([0,23]) based on
- linear OA(2542, 624, F25, 21) (dual of [624, 582, 22]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,23}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2529, 624, F25, 15) (dual of [624, 595, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2547, 624, F25, 24) (dual of [624, 577, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2524, 624, F25, 12) (dual of [624, 600, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {3,4,…,14}, and designed minimum distance d ≥ |I|+1 = 13 [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.