MinT - Information on Result #1050887

Information on Result #1050887

Linear OOA(81¹⁶, 6641, F₈₁, 4, 7) (dual of [(6641, 4), 26548, 8]-NRT-code), using OOA stacking with additional row based on linear OOA(81¹⁶, 6642, F₈₁, 3, 7) (dual of [(6642, 3), 19910, 8]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 3, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
3. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
4. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
5. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
6. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
7. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
8. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
9. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
10. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
11. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
12. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
13. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
14. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
15. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
16. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
17. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
18. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
19. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
20. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
21. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
22. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
23. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
24. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
25. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
26. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
27. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
28. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
29. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
30. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
31. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
32. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
33. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
34. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
35. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
36. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
37. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
38. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
39. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
40. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
41. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
42. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
43. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
44. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
45. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
46. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
47. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
48. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
49. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
50. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
51. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
52. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
53. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
54. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
55. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
56. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
57. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
58. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
59. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
60. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
61. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
62. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
63. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
64. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
65. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
66. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
67. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
68. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
69. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
70. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
71. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
72. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
73. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
74. linear OOA(81⁰, 82, F₈₁, 3, 0) (dual of [(82, 3), 246, 1]-NRT-code) (see above)
75. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 3, 1) for arbitrarily large s, using
    - appending 2 arbitrary columns [i] based on linear OA(81¹, s, F₈₁, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
76. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
77. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
78. linear OOA(81¹, 82, F₈₁, 3, 1) (dual of [(82, 3), 245, 2]-NRT-code) (see above)
79. linear OOA(81², 82, F₈₁, 3, 2) (dual of [(82, 3), 244, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;244,81) [i]
80. linear OOA(81³, 82, F₈₁, 3, 3) (dual of [(82, 3), 243, 4]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;243,81) [i]
81. linear OOA(81⁷, 82, F₈₁, 3, 7) (dual of [(82, 3), 239, 8]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;239,81) [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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(81⁶⁹, 2103791, F₈₁, 4, 14) (dual of [(2103791, 4), 8415095, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁷³, 2103791, F₈₁, 4, 15) (dual of [(2103791, 4), 8415091, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs