MinT - Information on Result #665378

Information on Result #665378

Linear OA(25¹⁶, 16250, F₂₅, 5) (dual of [16250, 16234, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 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, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25⁰, 650, F₂₅, 0) (dual of [650, 650, 1]-code) (see above)
linear OA(25¹, 650, F₂₅, 1) (dual of [650, 649, 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, 650, F₂₅, 1) (dual of [650, 649, 2]-code) (see above)
linear OA(25¹, 650, F₂₅, 1) (dual of [650, 649, 2]-code) (see above)
linear OA(25³, 650, F₂₅, 2) (dual of [650, 647, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(25³, 651, F₂₅, 2) (dual of [651, 648, 3]-code), using
  - Hamming code H(3,25) [i]
linear OA(25¹⁰, 650, F₂₅, 5) (dual of [650, 640, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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 (see above)
  2. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  3. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  4. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  5. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  6. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  7. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  8. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  9. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  10. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  11. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  12. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  13. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  14. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  15. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  16. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  17. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  18. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  19. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  20. linear OA(25⁰, 26, F₂₅, 0) (dual of [26, 26, 1]-code) (see above)
  21. 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 (see above)
  22. linear OA(25¹, 26, F₂₅, 1) (dual of [26, 25, 2]-code) (see above)
  23. linear OA(25¹, 26, F₂₅, 1) (dual of [26, 25, 2]-code) (see above)
  24. 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]
  25. linear OA(25⁵, 26, F₂₅, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
    - extended Reedâ€“Solomon code RS_e(21,25) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 26Â | 25²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
    - algebraic-geometric code AG(F,10P) with 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+6P) with degQ = 2 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.