MinT - Information on Result #670046

Information on Result #670046

Linear OA(81¹⁶, 538002, F₈₁, 5) (dual of [538002, 537986, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 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(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81⁰, 6642, F₈₁, 0) (dual of [6642, 6642, 1]-code) (see above)
linear OA(81¹, 6642, F₈₁, 1) (dual of [6642, 6641, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(81¹, 6642, F₈₁, 1) (dual of [6642, 6641, 2]-code) (see above)
linear OA(81¹, 6642, F₈₁, 1) (dual of [6642, 6641, 2]-code) (see above)
linear OA(81³, 6642, F₈₁, 2) (dual of [6642, 6639, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
  - Hamming code H(3,81) [i]
linear OA(81¹⁰, 6642, F₈₁, 5) (dual of [6642, 6632, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
  2. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  3. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  4. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  5. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  6. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  7. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  8. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  9. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  10. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  11. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  12. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  13. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  14. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  15. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  16. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  17. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  18. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  19. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  20. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  21. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  22. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  23. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  24. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  25. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  26. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  27. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  28. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  29. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  30. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  31. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  32. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  33. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  34. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  35. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  36. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  37. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  38. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  39. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  40. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  41. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  42. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  43. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  44. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  45. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  46. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  47. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  48. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  49. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  50. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  51. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  52. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  53. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  54. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  55. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  56. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  57. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  58. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  59. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  60. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  61. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  62. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  63. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  64. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  65. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  66. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  67. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  68. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  69. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  70. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  71. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  72. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  73. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  74. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  75. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  76. linear OA(81⁰, 82, F₈₁, 0) (dual of [82, 82, 1]-code) (see above)
  77. linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
  78. linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
  79. linear OA(81¹, 82, F₈₁, 1) (dual of [82, 81, 2]-code) (see above)
  80. linear OA(81², 82, F₈₁, 2) (dual of [82, 80, 3]-code or 82-arc in PG(1,81)), using
    - extended Reedâ€“Solomon code RS_e(80,81) [i]
    - Hamming code H(2,81) [i]
  81. linear OA(81⁵, 82, F₈₁, 5) (dual of [82, 77, 6]-code or 82-arc in PG(4,81)), using
    - extended Reedâ€“Solomon code RS_e(77,81) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 82Â | 81²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [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.