MinT - Information on Result #1022161

Information on Result #1022161

Linear OOA(64¹⁶, 266240, F₆₄, 3, 5) (dual of [(266240, 3), 798704, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64⁰, 4160, F₆₄, 3, 0) (dual of [(4160, 3), 12480, 1]-NRT-code) (see above)
linear OOA(64¹, 4160, F₆₄, 3, 1) (dual of [(4160, 3), 12479, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
  - appending 2 arbitrary columns [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]
linear OOA(64¹, 4160, F₆₄, 3, 1) (dual of [(4160, 3), 12479, 2]-NRT-code) (see above)
linear OOA(64¹, 4160, F₆₄, 3, 1) (dual of [(4160, 3), 12479, 2]-NRT-code) (see above)
linear OOA(64³, 4160, F₆₄, 3, 2) (dual of [(4160, 3), 12477, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 3, 2) (dual of [(4161, 3), 12480, 3]-NRT-code), using
  - appending 1 arbitrary column [i] 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]
linear OOA(64¹⁰, 4160, F₆₄, 3, 5) (dual of [(4160, 3), 12470, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s (see above)
  2. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  58. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  59. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  60. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s (see above)
  61. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code) (see above)
  62. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code) (see above)
  63. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
  64. linear OOA(64⁵, 65, F₆₄, 3, 5) (dual of [(65, 3), 190, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;190,64) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁵⁷, 3062441, F₆₄, 3, 11) (dual of [(3062441, 3), 9187266, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵³, 3062441, F₆₄, 3, 10) (dual of [(3062441, 3), 9187270, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs