MinT - Information on Result #1082389

Information on Result #1082389

Linear OOA(81⁵², 2366231, F₈₁, 4, 10) (dual of [(2366231, 4), 9464872, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁵, 269081, F₈₁, 4, 5) (dual of [(269081, 4), 1076309, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(81¹⁵, 269082, F₈₁, 2, 5) (dual of [(269082, 2), 538149, 6]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 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, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    3. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    4. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    5. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    6. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    7. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    8. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    9. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    10. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    11. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    12. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    13. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    14. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    15. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    16. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    17. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    18. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    19. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    20. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    21. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    22. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    23. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    24. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    25. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    26. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    27. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    28. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    29. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    30. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    31. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    32. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    33. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    34. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    35. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    36. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    37. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    38. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    39. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    40. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    41. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    42. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    43. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    44. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    45. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    46. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    47. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    48. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    49. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    50. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    51. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    52. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    53. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    54. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    55. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    56. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    57. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    58. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    59. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    60. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    61. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    62. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    63. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    64. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    65. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    66. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    67. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    68. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    69. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    70. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    71. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    72. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    73. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    74. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    75. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    76. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
    77. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 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]
    78. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
    79. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
    80. linear OOA(81³, 3322, F₈₁, 2, 2) (dual of [(3322, 2), 6641, 3]-NRT-code), using
      - discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
        appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
        Hamming code H(3,81) [i]
    81. linear OOA(81⁹, 3322, F₈₁, 2, 5) (dual of [(3322, 2), 6635, 6]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        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]
        linear OOA(81⁷, 3240, F₈₁, 2, 5) (dual of [(3240, 2), 6473, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81⁷, 6480, F₈₁, 5) (dual of [6480, 6473, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(81³⁷, 2097150, F₈₁, 4, 10) (dual of [(2097150, 4), 8388563, 11]-NRT-code), using
- OOA 4-folding [i] based on linear OA(81³⁷, 8388600, F₈₁, 10) (dual of [8388600, 8388563, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁶⁹, 4732462, F₈₁, 4, 10) (dual of [(4732462, 4), 18929779, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs