MinT - Information on Result #1050853

Information on Result #1050853

Linear OOA(81¹⁵, 269081, F₈₁, 4, 5) (dual of [(269081, 4), 1076309, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(81¹⁵, 269082, F₈₁, 2, 5) (dual of [(269082, 2), 538149, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81⁰, s, F₈₁, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
3. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
4. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
5. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
6. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
7. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
8. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
9. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
10. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
11. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
12. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
13. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
14. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
15. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
16. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
17. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
18. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
19. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
20. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
21. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
22. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
23. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
24. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
25. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
26. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
27. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
28. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
29. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
30. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
31. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
32. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
33. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
34. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
35. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
36. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
37. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
38. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
39. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
40. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
41. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
42. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
43. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
44. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
45. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
46. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
47. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
48. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
49. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
50. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
51. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
52. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
53. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
54. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
55. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
56. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
57. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
58. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
59. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
60. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
61. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
62. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
63. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
64. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
65. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
66. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
67. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
68. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
69. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
70. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
71. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
72. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
73. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
74. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
75. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
76. linear OOA(81⁰, 3322, F₈₁, 2, 0) (dual of [(3322, 2), 6644, 1]-NRT-code) (see above)
77. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81¹, s, F₈₁, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [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]
78. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
79. linear OOA(81¹, 3322, F₈₁, 2, 1) (dual of [(3322, 2), 6643, 2]-NRT-code) (see above)
80. linear OOA(81³, 3322, F₈₁, 2, 2) (dual of [(3322, 2), 6641, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(81³, 6643, F₈₁, 2, 2) (dual of [(6643, 2), 13283, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(81³, 6643, F₈₁, 2) (dual of [6643, 6640, 3]-code), using
      - Hamming code H(3,81) [i]
81. linear OOA(81⁹, 3322, F₈₁, 2, 5) (dual of [(3322, 2), 6635, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(81², 82, F₈₁, 2, 2) (dual of [(82, 2), 162, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;162,81) [i]
    2. linear OOA(81⁷, 3240, F₈₁, 2, 5) (dual of [(3240, 2), 6473, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(81⁷, 6480, F₈₁, 5) (dual of [6480, 6473, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [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(81⁵², 2366231, F₈₁, 4, 10) (dual of [(2366231, 4), 9464872, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁵⁶, 2366231, F₈₁, 4, 11) (dual of [(2366231, 4), 9464868, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs