MinT - Information on Result #1614285

Information on Result #1614285

Linear OOA(128¹⁵, 2097408, F₁₂₈, 4, 5) (dual of [(2097408, 4), 8389617, 6]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(128¹⁵, 2097408, F₁₂₈, 5) (dual of [2097408, 2097393, 6]-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 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, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
3. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
4. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
5. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
6. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
7. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
8. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
9. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
10. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
11. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
12. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
13. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
14. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
15. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
16. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
17. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
18. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
19. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
20. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
21. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
22. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
23. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
24. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
25. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
26. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
27. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
28. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
29. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
30. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
31. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
32. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
33. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
34. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
35. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
36. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
37. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
38. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
39. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
40. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
41. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
42. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
43. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
44. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
45. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
46. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
47. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
48. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
49. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
50. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
51. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
52. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
53. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
54. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
55. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
56. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
57. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
58. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
59. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
60. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
61. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
62. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
63. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
64. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
65. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
66. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
67. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
68. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
69. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
70. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
71. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
72. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
73. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
74. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
75. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
76. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
77. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
78. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
79. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
80. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
81. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
82. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
83. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
84. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
85. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
86. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
87. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
88. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
89. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
90. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
91. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
92. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
93. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
94. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
95. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
96. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
97. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
98. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
99. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
100. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
101. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
102. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
103. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
104. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
105. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
106. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
107. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
108. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
109. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
110. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
111. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
112. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
113. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
114. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
115. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
116. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
117. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
118. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
119. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
120. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
121. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
122. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
123. linear OA(128⁰, 16386, F₁₂₈, 0) (dual of [16386, 16386, 1]-code) (see above)
124. linear OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 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]
125. linear OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 2]-code) (see above)
126. linear OA(128¹, 16386, F₁₂₈, 1) (dual of [16386, 16385, 2]-code) (see above)
127. linear OA(128³, 16386, F₁₂₈, 2) (dual of [16386, 16383, 3]-code), using
  - discarding factors / shortening the dual code based on linear OA(128³, 16513, F₁₂₈, 2) (dual of [16513, 16510, 3]-code), using
    - Hamming code H(3,128) [i]
128. linear OA(128⁹, 16386, F₁₂₈, 5) (dual of [16386, 16377, 6]-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OA(128², 129, F₁₂₈, 2) (dual of [129, 127, 3]-code or 129-arc in PG(1,128)), using
      - extended Reedâ€“Solomon code RS_e(127,128) [i]
      - Hamming code H(2,128) [i]
    2. linear OA(128⁷, 16257, F₁₂₈, 5) (dual of [16257, 16250, 6]-code), using
      - a code by Danev and Olsson [i]

Mode: 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(128¹⁵, 2097408, F₁₂₈, 5, 5) (dual of [(2097408, 5), 10487025, 6]-NRT-code)	[i]		Appending kth Column