MinT - Information on Result #2807305

Information on Result #2807305

Linear OOA(128⁷⁸, large, F₁₂₈, 4, 9), using 7 times NRT-code embedding in larger space based on linear OOA(128⁵⁰, large, F₁₂₈, 4, 9), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128⁰, s, F₁₂₈, 4, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
3. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
4. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
5. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
6. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
7. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
8. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
9. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
10. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
11. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
12. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
13. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
14. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
15. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
16. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
17. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
18. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
19. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
20. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
21. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
22. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
23. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
24. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
25. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
26. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
27. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
28. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
29. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
30. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
31. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
32. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
33. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
34. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
35. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
36. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
37. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
38. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
39. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
40. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
41. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
42. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
43. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
44. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
45. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
46. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
47. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
48. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
49. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
50. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
51. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
52. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
53. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
54. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
55. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
56. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
57. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
58. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
59. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
60. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
61. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
62. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
63. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
64. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
65. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
66. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
67. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
68. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
69. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
70. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
71. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
72. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
73. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
74. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
75. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
76. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
77. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
78. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
79. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
80. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
81. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
82. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
83. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
84. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
85. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
86. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
87. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
88. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
89. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
90. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
91. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
92. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
93. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
94. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
95. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
96. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
97. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
98. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
99. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
100. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
101. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
102. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
103. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
104. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
105. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
106. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
107. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
108. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
109. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
110. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
111. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
112. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
113. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
114. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
115. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
116. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
117. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
118. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
119. linear OOA(128⁰, 524288, F₁₂₈, 4, 0) (dual of [(524288, 4), 2097152, 1]-NRT-code) (see above)
120. linear OOA(128¹, 524288, F₁₂₈, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128¹, s, F₁₂₈, 4, 1) for arbitrarily large s, using
    - appending 3 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]
121. linear OOA(128¹, 524288, F₁₂₈, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
122. linear OOA(128¹, 524288, F₁₂₈, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
123. linear OOA(128¹, 524288, F₁₂₈, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
124. linear OOA(128¹, 524288, F₁₂₈, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
125. linear OOA(128⁴, 524288, F₁₂₈, 4, 2) (dual of [(524288, 4), 2097148, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128⁴, 2113665, F₁₂₈, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
    - appending 2 arbitrary columns [i] based on linear OOA(128⁴, 2113665, F₁₂₈, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(128⁴, 2113665, F₁₂₈, 2) (dual of [2113665, 2113661, 3]-code), using
        Hamming code H(4,128) [i]
126. linear OOA(128⁶, 524288, F₁₂₈, 4, 3) (dual of [(524288, 4), 2097146, 4]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128⁶, 2130050, F₁₂₈, 4, 3) (dual of [(2130050, 4), 8520194, 4]-NRT-code), using
    - appending 1 arbitrary column [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(128⁶, 2130050, F₁₂₈, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁶, 2130050, F₁₂₈, 3) (dual of [2130050, 2130044, 4]-code or 2130050-cap in PG(5,128)), using
        large caps in PG(5,Â b) [i]
127. linear OOA(128¹⁰, 524288, F₁₂₈, 4, 4) (dual of [(524288, 4), 2097142, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(128¹⁰, 1048577, F₁₂₈, 4, 4) (dual of [(1048577, 4), 4194298, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(128¹⁰, 2097154, F₁₂₈, 4) (dual of [2097154, 2097144, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(128¹⁰, 2097155, F₁₂₈, 4) (dual of [2097155, 2097145, 5]-code), using
        constructionÂ X applied to C_e(3) âŠ‚ C_e(2) [i] based on
        linear OA(128¹⁰, 2097152, F₁₂₈, 4) (dual of [2097152, 2097142, 5]-code), using an extension C_e(3) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 4 [i]
        linear OA(128⁷, 2097152, F₁₂₈, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension C_e(2) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,2], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 3 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 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]
128. linear OOA(128²⁵, 524288, F₁₂₈, 4, 9) (dual of [(524288, 4), 2097127, 10]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(128²⁵, 2097152, F₁₂₈, 9) (dual of [2097152, 2097127, 10]-code), using
    - an extension C_e(8) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,8], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

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

None.