MinT - Information on Result #876258

Information on Result #876258

Linear OOA(81¹², 265801, F₈₁, 2, 4) (dual of [(265801, 2), 531590, 5]-NRT-code), using OOA 2-folding based on linear OA(81¹², 531602, F₈₁, 4) (dual of [531602, 531590, 5]-code), using

discarding factors / shortening the dual code based on linear OA(81¹², 531603, F₈₁, 4) (dual of [531603, 531591, 5]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
      - OA with only one run / dual of code without redundancy [i]
  2. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  3. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  4. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  5. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  6. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  7. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  8. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  9. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  10. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  11. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  12. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  13. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  14. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  15. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  16. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  17. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  18. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  19. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  20. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  21. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  22. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  23. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  24. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  25. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  26. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  27. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  28. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  29. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  30. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  31. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  32. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  33. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  34. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  35. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  36. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  37. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  38. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  39. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  40. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  41. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  42. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  43. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  44. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  45. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  46. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  47. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  48. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  49. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  50. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  51. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  52. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  53. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  54. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  55. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  56. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  57. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  58. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  59. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  60. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  61. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  62. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  63. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  64. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  65. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  66. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  67. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  68. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  69. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  70. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  71. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  72. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  73. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  74. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  75. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  76. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  77. linear OA(81⁰, 6563, F₈₁, 0) (dual of [6563, 6563, 1]-code) (see above)
  78. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  79. linear OA(81¹, 6563, F₈₁, 1) (dual of [6563, 6562, 2]-code) (see above)
  80. linear OA(81³, 6563, F₈₁, 2) (dual of [6563, 6560, 3]-code), using
    - discarding factors / shortening the dual code based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
      - Hamming code H(3,81) [i]
  81. linear OA(81⁷, 6563, F₈₁, 4) (dual of [6563, 6556, 5]-code), using
    - constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
      1. linear OA(81⁷, 6561, F₈₁, 4) (dual of [6561, 6554, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
      2. linear OA(81⁵, 6561, F₈₁, 3) (dual of [6561, 6556, 4]-code or 6561-cap in PG(4,81)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 6560Â = 81²âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
      3. linear OA(81⁰, 2, F₈₁, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁰, s, F₈₁, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)

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.