MinT - Information on Result #1018783

Information on Result #1018783

Linear OOA(81⁸¹, 2799522, F₈₁, 3, 16) (dual of [(2799522, 3), 8398485, 17]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81²⁰, 3321, F₈₁, 3, 8) (dual of [(3321, 3), 9943, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(81²⁰, 6642, F₈₁, 2, 8) (dual of [(6642, 2), 13264, 9]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
        OOA with only one run / dual of NRT-code without redundancy [i]
    2. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    3. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    4. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    5. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    6. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    7. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    8. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    9. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    10. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    11. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    12. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    13. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    14. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    15. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    16. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    17. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    18. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    19. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    20. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    21. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    22. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    23. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    24. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    25. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    26. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    27. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    28. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    29. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    30. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    31. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    32. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    33. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    34. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    35. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    36. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    37. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    38. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    39. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    40. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    41. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    42. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    43. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    44. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    45. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    46. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    47. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    48. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    49. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    50. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    51. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    52. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    53. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    54. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    55. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    56. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    57. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    58. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    59. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    60. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    61. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    62. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    63. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    64. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    65. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    66. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    67. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    68. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    69. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    70. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    71. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    72. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    73. linear OOA(81⁰, 82, F₈₁, 2, 0) (dual of [(82, 2), 164, 1]-NRT-code) (see above)
    74. linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
    75. linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
    76. linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
    77. linear OOA(81¹, 82, F₈₁, 2, 1) (dual of [(82, 2), 163, 2]-NRT-code) (see above)
    78. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
    79. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code) (see above)
    80. linear OOA(81⁴, 82, F₈₁, 2, 4) (dual of [(82, 2), 160, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;160,81) [i]
    81. linear OOA(81⁸, 82, F₈₁, 2, 8) (dual of [(82, 2), 156, 9]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;156,81) [i]
linear OOA(81⁶¹, 2796201, F₈₁, 3, 16) (dual of [(2796201, 3), 8388542, 17]-NRT-code), using
- OOA 3-folding [i] based on linear OA(81⁶¹, large, F₈₁, 16) (dual of [large, large−61, 17]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

None.