MinT - Information on Result #907015

Information on Result #907015

Linear OOA(64⁵⁷, 4460541, F₆₄, 2, 11) (dual of [(4460541, 2), 8921025, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁶, 266240, F₆₄, 2, 5) (dual of [(266240, 2), 532464, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  58. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  59. linear OOA(64⁰, 4160, F₆₄, 2, 0) (dual of [(4160, 2), 8320, 1]-NRT-code) (see above)
  60. linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  61. linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code) (see above)
  62. linear OOA(64¹, 4160, F₆₄, 2, 1) (dual of [(4160, 2), 8319, 2]-NRT-code) (see above)
  63. linear OOA(64³, 4160, F₆₄, 2, 2) (dual of [(4160, 2), 8317, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
        Hamming code H(3,64) [i]
  64. linear OOA(64¹⁰, 4160, F₆₄, 2, 5) (dual of [(4160, 2), 8310, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s (see above)
      2. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      3. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      4. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      5. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      6. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      7. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      8. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      9. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      10. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      11. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      12. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      13. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      14. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      15. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      16. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      17. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      18. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      19. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      20. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      21. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      22. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      23. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      24. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      25. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      26. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      27. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      28. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      29. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      30. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      31. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      32. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      33. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      34. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      35. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      36. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      37. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      38. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      39. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      40. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      41. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      42. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      43. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      44. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      45. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      46. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      47. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      48. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      49. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      50. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      51. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      52. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      53. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      54. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      55. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      56. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      57. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      58. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      59. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
      60. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s (see above)
      61. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
      62. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
      63. linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
      64. linear OOA(64⁵, 65, F₆₄, 2, 5) (dual of [(65, 2), 125, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;125,64) [i]
linear OOA(64⁴¹, 4194301, F₆₄, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁴¹, 8388602, F₆₄, 11) (dual of [8388602, 8388561, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.