MinT - Information on Result #907197

Information on Result #907197

Linear OOA(128⁵⁶, 5251197, F₁₂₈, 2, 11) (dual of [(5251197, 2), 10502338, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(128¹⁵, 1056896, F₁₂₈, 2, 5) (dual of [(1056896, 2), 2113777, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  3. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  4. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  5. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  6. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  7. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  8. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  9. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  10. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  11. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  12. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  13. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  14. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  15. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  16. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  17. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  18. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  19. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  20. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  21. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  22. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  23. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  24. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  25. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  26. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  27. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  28. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  29. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  30. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  31. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  32. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  33. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  34. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  35. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  36. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  37. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  38. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  39. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  40. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  41. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  42. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  43. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  44. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  45. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  46. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  47. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  48. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  49. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  50. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  51. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  52. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  53. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  54. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  55. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  56. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  57. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  58. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  59. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  60. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  61. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  62. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  63. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  64. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  65. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  66. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  67. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  68. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  69. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  70. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  71. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  72. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  73. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  74. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  75. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  76. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  77. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  78. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  79. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  80. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  81. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  82. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  83. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  84. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  85. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  86. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  87. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  88. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  89. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  90. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  91. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  92. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  93. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  94. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  95. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  96. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  97. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  98. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  99. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  100. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  101. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  102. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  103. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  104. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  105. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  106. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  107. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  108. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  109. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  110. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  111. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  112. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  113. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  114. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  115. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  116. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  117. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  118. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  119. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  120. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  121. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  122. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  123. linear OOA(128⁰, 8257, F₁₂₈, 2, 0) (dual of [(8257, 2), 16514, 1]-NRT-code) (see above)
  124. linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [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]
  125. linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code) (see above)
  126. linear OOA(128¹, 8257, F₁₂₈, 2, 1) (dual of [(8257, 2), 16513, 2]-NRT-code) (see above)
  127. linear OOA(128³, 8257, F₁₂₈, 2, 2) (dual of [(8257, 2), 16511, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(128³, 16513, F₁₂₈, 2, 2) (dual of [(16513, 2), 33023, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
        Hamming code H(3,128) [i]
  128. linear OOA(128⁹, 8257, F₁₂₈, 2, 5) (dual of [(8257, 2), 16505, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(128², 129, F₁₂₈, 2, 2) (dual of [(129, 2), 256, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;256,128) [i]
      2. linear OOA(128⁷, 8128, F₁₂₈, 2, 5) (dual of [(8128, 2), 16249, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(128⁷, 16256, F₁₂₈, 5) (dual of [16256, 16249, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
        a code by Danev and Olsson [i]
linear OOA(128⁴¹, 4194301, F₁₂₈, 2, 11) (dual of [(4194301, 2), 8388561, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(128⁴¹, 8388602, F₁₂₈, 11) (dual of [8388602, 8388561, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴¹, large, F₁₂₈, 11) (dual of [large, large−41, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’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.

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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(128⁵⁶, 2625598, F₁₂₈, 4, 11) (dual of [(2625598, 4), 10502336, 12]-NRT-code)	[i]		OOA Folding