Information on Result #724800
Linear OA(25106, 661, F25, 49) (dual of [661, 555, 50]-code), using construction XX applied to C1 = C([614,34]), C2 = C([0,38]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([614,38]) based on
- linear OA(2586, 624, F25, 45) (dual of [624, 538, 46]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−10,−9,…,34}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2594, 624, F25, 49) (dual of [624, 530, 50]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−10,−9,…,38}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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(253, 11, F25, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,25) or 11-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), 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.