Information on Result #665579
Linear OA(2576, 680, F25, 28) (dual of [680, 604, 29]-code), using (u, u−v, u+v+w)-construction based on
- 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(2515, 29, F25, 14) (dual of [29, 14, 15]-code), using
- construction X applied to AG(F, Q+4P) ⊂ AG(F, Q+5P) [i] based on
- linear OA(2514, 26, F25, 14) (dual of [26, 12, 15]-code or 26-arc in PG(13,25)), using algebraic-geometric code AG(F, Q+4P) 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(2512, 26, F25, 12) (dual of [26, 14, 13]-code or 26-arc in PG(11,25)), using algebraic-geometric code AG(F, Q+5P) 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(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to AG(F, Q+4P) ⊂ AG(F, Q+5P) [i] based on
- linear OA(2552, 625, F25, 28) (dual of [625, 573, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
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.