MinT - Information on Result #671298

Information on Result #671298

Linear OA(128⁶⁸, 2097409, F₁₂₈, 19) (dual of [2097409, 2097341, 20]-code), using (u,Â u+v)-construction based on

linear OA(128¹³, 256, F₁₂₈, 9) (dual of [256, 243, 10]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 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]
  2. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  3. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  4. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  5. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  6. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  7. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  8. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  9. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  10. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  11. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  12. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  13. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  14. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  15. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  16. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  17. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  18. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  19. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  20. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  21. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  22. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  23. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  24. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  25. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  26. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  27. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  28. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  29. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  30. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  31. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  32. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  33. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  34. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  35. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  36. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  37. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  38. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  39. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  40. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  41. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  42. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  43. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  44. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  45. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  46. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  47. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  48. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  49. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  50. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  51. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  52. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  53. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  54. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  55. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  56. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  57. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  58. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  59. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  60. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  61. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  62. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  63. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  64. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  65. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  66. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  67. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  68. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  69. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  70. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  71. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  72. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  73. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  74. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  75. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  76. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  77. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  78. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  79. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  80. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  81. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  82. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  83. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  84. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  85. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  86. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  87. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  88. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  89. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  90. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  91. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  92. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  93. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  94. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  95. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  96. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  97. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  98. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  99. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  100. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  101. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  102. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  103. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  104. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  105. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  106. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  107. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  108. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  109. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  110. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  111. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  112. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  113. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  114. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  115. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  116. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  117. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  118. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  119. linear OA(128⁰, 2, F₁₂₈, 0) (dual of [2, 2, 1]-code) (see above)
  120. linear OA(128¹, 2, F₁₂₈, 1) (dual of [2, 1, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
  121. linear OA(128¹, 2, F₁₂₈, 1) (dual of [2, 1, 2]-code) (see above)
  122. linear OA(128¹, 2, F₁₂₈, 1) (dual of [2, 1, 2]-code) (see above)
  123. linear OA(128¹, 2, F₁₂₈, 1) (dual of [2, 1, 2]-code) (see above)
  124. linear OA(128¹, 2, F₁₂₈, 1) (dual of [2, 1, 2]-code) (see above)
  125. linear OA(128², 2, F₁₂₈, 2) (dual of [2, 0, 3]-code or 2-arc in PG(1,128)), using
    - complete OA / dual of code with only one code word [i]
  126. linear OA(128², 2, F₁₂₈, 2) (dual of [2, 0, 3]-code or 2-arc in PG(1,128)) (see above)
  127. linear OA(128², 2, F₁₂₈, 2) (dual of [2, 0, 3]-code or 2-arc in PG(1,128)) (see above)
  128. linear OA(128², 2, F₁₂₈, 2) (dual of [2, 0, 3]-code or 2-arc in PG(1,128)) (see above)
linear OA(128⁵⁵, 2097153, F₁₂₈, 19) (dual of [2097153, 2097098, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 2097153Â | 128⁶âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]

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.