MinT - Information on Result #2521496

Information on Result #2521496

Linear OOA(81⁷⁶, large, F₈₁, 2, 7), using 81¹ times duplication based on linear OOA(81⁷⁵, large, F₈₁, 2, 7), using

21 times NRT-code embedding in larger space [i] based on linear OOA(81³³, large, F₈₁, 2, 7), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  3. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  4. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  5. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  6. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  7. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  8. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  9. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  10. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  11. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  12. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  13. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  14. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  15. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  16. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  17. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  18. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  19. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  20. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  21. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  22. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  23. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  24. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  25. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  26. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  27. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  28. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  29. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  30. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  31. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  32. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  33. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  34. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  35. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  36. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  37. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  38. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  39. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  40. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  41. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  42. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  43. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  44. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  45. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  46. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  47. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  48. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  49. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  50. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  51. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  52. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  53. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  54. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  55. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  56. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  57. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  58. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  59. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  60. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  61. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  62. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  63. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  64. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  65. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  66. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  67. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  68. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  69. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  70. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  71. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  72. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  73. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  74. linear OOA(81⁰, 265722, F₈₁, 2, 0) (dual of [(265722, 2), 531444, 1]-NRT-code) (see above)
  75. linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  76. linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
  77. linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
  78. linear OOA(81¹, 265722, F₈₁, 2, 1) (dual of [(265722, 2), 531443, 2]-NRT-code) (see above)
  79. linear OOA(81⁴, 265722, F₈₁, 2, 2) (dual of [(265722, 2), 531440, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 538084, F₈₁, 2, 2) (dual of [(538084, 2), 1076164, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(81⁴, 538084, F₈₁, 2) (dual of [538084, 538080, 3]-code), using
        Hamming code H(4,81) [i]
  80. linear OOA(81⁶, 265722, F₈₁, 2, 3) (dual of [(265722, 2), 531438, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁶, 538248, F₈₁, 2, 3) (dual of [(538248, 2), 1076490, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁶, 538248, F₈₁, 3) (dual of [538248, 538242, 4]-code or 538248-cap in PG(5,81)), using
        large caps in PG(5,Â b) [i]
  81. linear OOA(81¹⁹, 265722, F₈₁, 2, 7) (dual of [(265722, 2), 531425, 8]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(81¹⁹, 531444, F₈₁, 7) (dual of [531444, 531425, 8]-code), using
      - constructionÂ X applied to C_e(6) âŠ‚ C_e(5) [i] based on
        linear OA(81¹⁹, 531441, F₈₁, 7) (dual of [531441, 531422, 8]-code), using an extension C_e(6) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,6], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OA(81¹⁶, 531441, F₈₁, 6) (dual of [531441, 531425, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 81³âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(81⁰, 3, F₈₁, 0) (dual of [3, 3, 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]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.