MinT - Information on Result #669048

Information on Result #669048

Linear OA(49¹⁶, 120050, F₄₉, 5) (dual of [120050, 120034, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 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(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49⁰, 2450, F₄₉, 0) (dual of [2450, 2450, 1]-code) (see above)
linear OA(49¹, 2450, F₄₉, 1) (dual of [2450, 2449, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(49¹, 2450, F₄₉, 1) (dual of [2450, 2449, 2]-code) (see above)
linear OA(49¹, 2450, F₄₉, 1) (dual of [2450, 2449, 2]-code) (see above)
linear OA(49³, 2450, F₄₉, 2) (dual of [2450, 2447, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(49³, 2451, F₄₉, 2) (dual of [2451, 2448, 3]-code), using
  - Hamming code H(3,49) [i]
linear OA(49¹⁰, 2450, F₄₉, 5) (dual of [2450, 2440, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(49⁰, s, F₄₉, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
  2. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  3. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  4. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  5. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  6. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  7. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  8. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  9. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  10. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  11. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  12. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  13. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  14. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  15. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  16. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  17. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  18. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  19. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  20. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  21. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  22. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  23. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  24. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  25. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  26. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  27. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  28. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  29. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  30. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  31. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  32. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  33. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  34. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  35. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  36. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  37. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  38. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  39. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  40. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  41. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  42. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  43. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  44. linear OA(49⁰, 50, F₄₉, 0) (dual of [50, 50, 1]-code) (see above)
  45. linear OA(49¹, 50, F₄₉, 1) (dual of [50, 49, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
  46. linear OA(49¹, 50, F₄₉, 1) (dual of [50, 49, 2]-code) (see above)
  47. linear OA(49¹, 50, F₄₉, 1) (dual of [50, 49, 2]-code) (see above)
  48. linear OA(49², 50, F₄₉, 2) (dual of [50, 48, 3]-code or 50-arc in PG(1,49)), using
    - extended Reedâ€“Solomon code RS_e(48,49) [i]
    - Hamming code H(2,49) [i]
    - algebraic-geometric code AG(F, Q+22P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using the rational function field F₄₉(x) [i]
  49. linear OA(49⁵, 50, F₄₉, 5) (dual of [50, 45, 6]-code or 50-arc in PG(4,49)), using
    - extended Reedâ€“Solomon code RS_e(45,49) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 50Â | 49²âˆ’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,22P) with degPÂ =Â 2 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
    - algebraic-geometric code AG(F, Q+14P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (see above)
    - algebraic-geometric code AG(F, Q+8P) with degQ = 4 and degPÂ =Â 5 [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50 (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.