MinT - Information on Result #1708051

Information on Result #1708051

Linear OOA(81¹⁵, 531603, F₈₁, 5, 5) (dual of [(531603, 5), 2658000, 6]-NRT-code), using appending kth column based on linear OOA(81¹⁵, 531603, F₈₁, 4, 5) (dual of [(531603, 4), 2126397, 6]-NRT-code), using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(81¹⁵, 531603, F₈₁, 5) (dual of [531603, 531588, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 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]
  2. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  3. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  4. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  5. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  6. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  7. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  8. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  9. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  10. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  11. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  12. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  13. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  14. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  15. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  16. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  17. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  18. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  19. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  20. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  21. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  22. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  23. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  24. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  25. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  26. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  27. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  28. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  29. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  30. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  31. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  32. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  33. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  34. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  35. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  36. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  37. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  38. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  39. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  40. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  41. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  42. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  43. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  44. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  45. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  46. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  47. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  48. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  49. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  50. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  51. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  52. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  53. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  54. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  55. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  56. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  57. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  58. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  59. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  60. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  61. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  62. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  63. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  64. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  65. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  66. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  67. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  68. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  69. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  70. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  71. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  72. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  73. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  74. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  75. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  76. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  77. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 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]
  78. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code) (see above)
  79. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code) (see above)
  80. linear OA(81³, 6563, F₈₁, 2) (dual of [6563, 6560, 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]
  81. linear OA(81⁹, 6563, F₈₁, 5) (dual of [6563, 6554, 6]-code), using
    - (u,Â u+v)-construction [i] based on
      1. 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]
      2. linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]

Mode: Linear.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (10, 15, 531603)-net over F₈₁	[i]		Net Defined by OOA