MinT - Information on Result #1022509

Information on Result #1022509

Linear OOA(64⁵², 2929385, F₆₄, 3, 10) (dual of [(2929385, 3), 8788103, 11]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁵, 133184, F₆₄, 3, 5) (dual of [(133184, 3), 399537, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 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]
  2. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  58. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  59. linear OOA(64⁰, 2081, F₆₄, 3, 0) (dual of [(2081, 3), 6243, 1]-NRT-code) (see above)
  60. linear OOA(64¹, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 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]
  61. linear OOA(64¹, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 2]-NRT-code) (see above)
  62. linear OOA(64¹, 2081, F₆₄, 3, 1) (dual of [(2081, 3), 6242, 2]-NRT-code) (see above)
  63. linear OOA(64³, 2081, F₆₄, 3, 2) (dual of [(2081, 3), 6240, 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]
  64. linear OOA(64⁹, 2081, F₆₄, 3, 5) (dual of [(2081, 3), 6234, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. 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]
      2. linear OOA(64⁷, 2016, F₆₄, 3, 5) (dual of [(2016, 3), 6041, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(64³⁷, 2796201, F₆₄, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64³⁷, large, F₆₄, 10) (dual of [large, large−37, 11]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’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.