Information on Result #1022658

Linear OOA(12860, large, F128, 3, 10), using generalized (u, u+v)-construction based on
  1. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code), using
  2. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  3. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  4. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  5. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  6. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  7. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  8. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  9. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  10. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  11. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  12. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  13. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  14. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  15. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  16. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  17. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  18. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  19. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  20. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  21. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  22. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  23. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  24. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  25. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  26. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  27. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  28. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  29. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  30. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  31. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  32. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  33. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  34. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  35. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  36. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  37. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  38. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  39. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  40. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  41. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  42. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  43. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  44. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  45. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  46. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  47. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  48. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  49. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  50. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  51. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  52. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  53. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  54. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  55. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  56. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  57. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  58. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  59. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  60. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  61. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  62. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  63. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  64. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  65. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  66. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  67. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  68. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  69. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  70. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  71. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  72. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  73. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  74. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  75. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  76. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  77. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  78. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  79. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  80. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  81. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  82. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  83. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  84. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  85. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  86. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  87. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  88. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  89. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  90. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  91. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  92. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  93. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  94. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  95. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  96. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  97. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  98. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  99. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  100. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  101. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  102. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  103. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  104. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  105. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  106. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  107. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  108. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  109. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  110. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  111. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  112. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  113. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  114. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  115. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  116. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  117. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  118. linear OOA(1280, 699051, F128, 3, 0) (dual of [(699051, 3), 2097153, 1]-NRT-code) (see above)
  119. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
  120. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
  121. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
  122. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
  123. linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
  124. linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code), using
  125. linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code) (see above)
  126. linear OOA(1286, 699051, F128, 3, 3) (dual of [(699051, 3), 2097147, 4]-NRT-code), using
  127. linear OOA(12813, 699051, F128, 3, 5) (dual of [(699051, 3), 2097140, 6]-NRT-code), using
  128. linear OOA(12828, 699051, F128, 3, 10) (dual of [(699051, 3), 2097125, 11]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(12828, 2097153, F128, 10) (dual of [2097153, 2097125, 11]-code), using
      • discarding factors / shortening the dual code based on linear OA(12828, 2097155, F128, 10) (dual of [2097155, 2097127, 11]-code), using
        • construction X applied to Ce(9) ⊂ Ce(8) [i] based on
          1. linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
          2. linear OA(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
          3. linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code) (see above)

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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(12860, large, F128, 3, 9) [i]Strength Reduction for OOAs
2Linear OOA(12860, large, F128, 3, 8) [i]
3Linear OOA(12860, large, F128, 3, 7) [i]
4Linear OOA(12860, large, F128, 3, 6) [i]
5Linear OOA(12860, large, F128, 3, 5) [i]
6Linear OOA(12860, large, F128, 3, 4) [i]
7Linear OOA(12860, large, F128, 3, 3) [i]
8Linear OOA(12863, large, F128, 3, 10) [i]NRT-Code Embedding in Larger Space
9Linear OOA(12866, large, F128, 3, 10) [i]
10Linear OOA(12869, large, F128, 3, 10) [i]
11Linear OOA(12872, large, F128, 3, 10) [i]
12Linear OOA(12875, large, F128, 3, 10) [i]
13Linear OOA(12878, large, F128, 3, 10) [i]
14Linear OOA(12861, large, F128, 3, 10) [i]OOA Duplication
15Linear OOA(12862, large, F128, 3, 10) [i]
16Linear OOA(12860, 4194301, F128, 15, 10) (dual of [(4194301, 15), 62914455, 11]-NRT-code) [i]OOA Folding and Stacking with Additional Row