MinT - Information on Result #1068637

Information on Result #1068637

Linear OOA(81⁵², 2231691, F₈₁, 4, 10) (dual of [(2231691, 4), 8926712, 11]-NRT-code), using OOA 2-folding based on linear OOA(81⁵², 4463382, F₈₁, 2, 10) (dual of [(4463382, 2), 8926712, 11]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(81⁵², 4463383, F₈₁, 2, 10) (dual of [(4463383, 2), 8926714, 11]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(81³⁷, 4194301, F₈₁, 2, 10) (dual of [(4194301, 2), 8388565, 11]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81³⁷, 8388602, F₈₁, 10) (dual of [8388602, 8388565, 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

None.