MinT - Information on Result #1084921

Information on Result #1084921

Linear OOA(128⁷⁸, 4210812, F₁₂₈, 4, 13) (dual of [(4210812, 4), 16843170, 14]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(128⁸, 16512, F₁₂₈, 4, 4) (dual of [(16512, 4), 66040, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(128⁸, 16512, F₁₂₈, 3, 4) (dual of [(16512, 3), 49528, 5]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 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, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    3. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    4. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    5. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    6. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    7. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    8. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    9. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    10. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    11. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    12. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    13. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    14. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    15. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    16. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    17. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    18. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    19. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    20. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    21. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    22. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    23. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    24. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    25. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    26. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    27. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    28. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    29. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    30. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    31. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    32. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    33. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    34. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    35. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    36. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    37. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    38. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    39. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    40. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    41. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    42. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    43. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    44. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    45. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    46. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    47. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    48. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    49. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    50. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    51. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    52. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    53. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    54. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    55. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    56. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    57. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    58. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    59. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    60. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    61. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    62. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    63. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    64. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    65. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    66. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    67. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    68. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    69. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    70. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    71. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    72. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    73. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    74. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    75. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    76. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    77. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    78. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    79. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    80. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    81. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    82. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    83. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    84. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    85. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    86. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    87. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    88. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    89. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    90. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    91. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    92. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    93. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    94. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    95. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    96. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    97. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    98. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    99. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    100. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    101. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    102. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    103. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    104. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    105. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    106. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    107. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    108. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    109. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    110. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    111. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    112. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    113. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    114. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    115. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    116. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    117. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    118. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    119. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    120. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    121. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    122. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    123. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    124. linear OOA(128⁰, 129, F₁₂₈, 3, 0) (dual of [(129, 3), 387, 1]-NRT-code) (see above)
    125. linear OOA(128¹, 129, F₁₂₈, 3, 1) (dual of [(129, 3), 386, 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]
    126. linear OOA(128¹, 129, F₁₂₈, 3, 1) (dual of [(129, 3), 386, 2]-NRT-code) (see above)
    127. linear OOA(128², 129, F₁₂₈, 3, 2) (dual of [(129, 3), 385, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;385,128) [i]
    128. linear OOA(128⁴, 129, F₁₂₈, 3, 4) (dual of [(129, 3), 383, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(3;383,128) [i]
linear OOA(128²¹, 2097150, F₁₂₈, 4, 6) (dual of [(2097150, 4), 8388579, 7]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(128²¹, 2796201, F₁₂₈, 4, 6) (dual of [(2796201, 4), 11184783, 7]-NRT-code), using
  - OA 3-folding and stacking [i] based on linear OA(128²¹, large, F₁₂₈, 6) (dual of [large, large−21, 7]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 17895697Â | 128⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(128⁴⁹, 2097150, F₁₂₈, 4, 13) (dual of [(2097150, 4), 8388551, 14]-NRT-code), using
- OOA 4-folding [i] based on linear OA(128⁴⁹, 8388600, F₁₂₈, 13) (dual of [8388600, 8388551, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(128⁴⁹, large, F₁₂₈, 13) (dual of [large, large−49, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 15790321Â | 128⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.