MinT - Information on Result #1203355

Information on Result #1203355

Linear OOA(128⁶³, 3795878, F₁₂₈, 15, 11) (dual of [(3795878, 15), 56938107, 12]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(128⁶³, 7591757, F₁₂₈, 3, 11) (dual of [(7591757, 3), 22775208, 12]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(128⁶³, 7591758, F₁₂₈, 3, 11) (dual of [(7591758, 3), 22775211, 12]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 3, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  3. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  4. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  5. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  6. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  7. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  8. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  9. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  10. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  11. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  12. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  13. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  14. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  15. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  16. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  17. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  18. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  19. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  20. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  21. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  22. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  23. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  24. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  25. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  26. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  27. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  28. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  29. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  30. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  31. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  32. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  33. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  34. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  35. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  36. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  37. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  38. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  39. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  40. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  41. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  42. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  43. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  44. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  45. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  46. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  47. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  48. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  49. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  50. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  51. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  52. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  53. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  54. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  55. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  56. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  57. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  58. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  59. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  60. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  61. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  62. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  63. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  64. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  65. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  66. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  67. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  68. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  69. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  70. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  71. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  72. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  73. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  74. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  75. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  76. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  77. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  78. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  79. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  80. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  81. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  82. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  83. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  84. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  85. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  86. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  87. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  88. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  89. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  90. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  91. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  92. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  93. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  94. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  95. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  96. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  97. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  98. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  99. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  100. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  101. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  102. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  103. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  104. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  105. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  106. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  107. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  108. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  109. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  110. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  111. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  112. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  113. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  114. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  115. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  116. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  117. linear OOA(128⁰, 49156, F₁₂₈, 3, 0) (dual of [(49156, 3), 147468, 1]-NRT-code) (see above)
  118. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  119. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
  120. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
  121. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
  122. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
  123. linear OOA(128¹, 49156, F₁₂₈, 3, 1) (dual of [(49156, 3), 147467, 2]-NRT-code) (see above)
  124. linear OOA(128⁴, 49156, F₁₂₈, 3, 2) (dual of [(49156, 3), 147464, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
      - appending 1 arbitrary column [i] based on linear OOA(128⁴, 2113665, F₁₂₈, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
        appending kth column [i] based on linear OA(128⁴, 2113665, F₁₂₈, 2) (dual of [2113665, 2113661, 3]-code), using
        Hamming code H(4,128) [i]
  125. linear OOA(128⁴, 49156, F₁₂₈, 3, 2) (dual of [(49156, 3), 147464, 3]-NRT-code) (see above)
  126. linear OOA(128⁵, 49156, F₁₂₈, 3, 3) (dual of [(49156, 3), 147463, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(128⁵, 49156, F₁₂₈, 2, 3) (dual of [(49156, 2), 98307, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁵, 49156, F₁₂₈, 3) (dual of [49156, 49151, 4]-code or 49156-cap in PG(4,128)), using
        large caps in PG(4,Â b) [i]
  127. linear OOA(128¹³, 699051, F₁₂₈, 3, 5) (dual of [(699051, 3), 2097140, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128¹³, 1048577, F₁₂₈, 3, 5) (dual of [(1048577, 3), 3145718, 6]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OA(128¹³, 2097155, F₁₂₈, 5) (dual of [2097155, 2097142, 6]-code), using
        constructionÂ X applied to C_e(4) âŠ‚ C_e(3) [i] based on
        linear OA(128¹³, 2097152, F₁₂₈, 5) (dual of [2097152, 2097139, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  128. linear OOA(128³¹, 699051, F₁₂₈, 3, 11) (dual of [(699051, 3), 2097122, 12]-NRT-code), using
    - OOA 3-folding [i] based on linear OA(128³¹, 2097153, F₁₂₈, 11) (dual of [2097153, 2097122, 12]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (52, 63, 3795878)-net over F₁₂₈	[i]		Net Defined by OOA