MinT - Information on Result #665374

Information on Result #665374

Linear OA(25¹⁴, 650, F₂₅, 6) (dual of [650, 636, 7]-code), using generalized (u,Â u+v)-construction based on

linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(25⁰, s, F₂₅, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
linear OA(25¹, 26, F₂₅, 1) (dual of [26, 25, 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
  - parity-check code [i]
linear OA(25¹, 26, F₂₅, 1) (dual of [26, 25, 2]-code) (see above)
linear OA(25¹, 26, F₂₅, 1) (dual of [26, 25, 2]-code) (see above)
linear OA(25², 26, F₂₅, 2) (dual of [26, 24, 3]-code or 26-arc in PG(1,25)), using
- extended Reedâ€“Solomon code RS_e(24,25) [i]
- Hamming code H(2,25) [i]
- algebraic-geometric code AG(F, Q+10P) 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]
linear OA(25³, 26, F₂₅, 3) (dual of [26, 23, 4]-code or 26-arc in PG(2,25) or 26-cap in PG(2,25)), using
- extended Reedâ€“Solomon code RS_e(23,25) [i]
- oval in PG(2,Â 25) [i]
- algebraic-geometric code AG(F, Q+6P) 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(25⁶, 26, F₂₅, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using
- extended Reedâ€“Solomon code RS_e(20,25) [i]
- algebraic-geometric code AG(F, Q+8P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)
- algebraic-geometric code AG(F, Q+5P) with degQ = 4 and degPÂ =Â 3 [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26 (see above)

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.