MinT - Information on Result #1022632

Information on Result #1022632

Linear OOA(81⁷⁵, 2802879, F₈₁, 3, 15) (dual of [(2802879, 3), 8408562, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(81¹⁸, 6678, F₈₁, 3, 7) (dual of [(6678, 3), 20016, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 3, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  3. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  4. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  5. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  6. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  7. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  8. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  9. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  10. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  11. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  12. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  13. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  14. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  15. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  16. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  17. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  18. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  19. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  20. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  21. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  22. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  23. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  24. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  25. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  26. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  27. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  28. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  29. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  30. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  31. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  32. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  33. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  34. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  35. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  36. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  37. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  38. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  39. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  40. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  41. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  42. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  43. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  44. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  45. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  46. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  47. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  48. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  49. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  50. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  51. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  52. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  53. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  54. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  55. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  56. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  57. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  58. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  59. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  60. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  61. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  62. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  63. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  64. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  65. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  66. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  67. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  68. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  69. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  70. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  71. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  72. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  73. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  74. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
  75. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [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, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
  77. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
  78. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
  79. linear OOA(81², 82, F₈₁, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;244,81) [i]
  80. linear OOA(81⁴, 100, F₈₁, 3, 3) (dual of [(100, 3), 296, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(81⁴, 6561, F₈₁, 3, 3) (dual of [(6561, 3), 19679, 4]-NRT-code), using
      - OOA stacking with additional row [i] based on linear OA(81⁴, 6562, F₈₁, 3) (dual of [6562, 6558, 4]-code or 6562-cap in PG(3,81)), using
        ovoid in PG(3,Â 81) [i]
  81. linear OOA(81⁸, 100, F₈₁, 3, 7) (dual of [(100, 3), 292, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,292P) [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]
linear OOA(81⁵⁷, 2796201, F₈₁, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
- OOA 3-folding [i] based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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

None.