MinT - Information on Result #669376

Information on Result #669376

Linear OA(64¹⁶, 266240, F₆₄, 5) (dual of [266240, 266224, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64⁰, 4160, F₆₄, 0) (dual of [4160, 4160, 1]-code) (see above)
linear OA(64¹, 4160, F₆₄, 1) (dual of [4160, 4159, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(64¹, 4160, F₆₄, 1) (dual of [4160, 4159, 2]-code) (see above)
linear OA(64¹, 4160, F₆₄, 1) (dual of [4160, 4159, 2]-code) (see above)
linear OA(64³, 4160, F₆₄, 2) (dual of [4160, 4157, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
  - Hamming code H(3,64) [i]
linear OA(64¹⁰, 4160, F₆₄, 5) (dual of [4160, 4150, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁰, s, F₆₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
  2. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  3. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  4. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  5. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  6. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  7. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  8. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  9. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  10. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  11. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  12. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  13. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  14. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  15. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  16. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  17. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  18. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  19. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  20. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  21. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  22. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  23. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  24. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  25. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  26. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  27. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  28. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  29. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  30. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  31. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  32. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  33. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  34. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  35. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  36. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  37. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  38. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  39. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  40. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  41. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  42. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  43. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  44. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  45. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  46. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  47. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  48. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  49. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  50. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  51. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  52. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  53. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  54. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  55. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  56. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  57. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  58. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  59. linear OA(64⁰, 65, F₆₄, 0) (dual of [65, 65, 1]-code) (see above)
  60. linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
  61. linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
  62. linear OA(64¹, 65, F₆₄, 1) (dual of [65, 64, 2]-code) (see above)
  63. linear OA(64², 65, F₆₄, 2) (dual of [65, 63, 3]-code or 65-arc in PG(1,64)), using
    - extended Reedâ€“Solomon code RS_e(63,64) [i]
    - Hamming code H(2,64) [i]
  64. linear OA(64⁵, 65, F₆₄, 5) (dual of [65, 60, 6]-code or 65-arc in PG(4,64)), using
    - extended Reedâ€“Solomon code RS_e(60,64) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.