MinT - Information on Result #1017705

Information on Result #1017705

Linear OOA(64⁵⁷, 3062440, F₆₄, 3, 11) (dual of [(3062440, 3), 9187263, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁶, 266239, F₆₄, 3, 5) (dual of [(266239, 3), 798701, 6]-NRT-code), using
- OOA stacking with additional row [i] 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
        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)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
        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)
        linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
        linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
        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]
        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, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
- OOA 3-folding [i] 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(64⁷⁴, 6124880, F₆₄, 3, 11) (dual of [(6124880, 3), 18374566, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs