MinT - Information on Result #944821

Information on Result #944821

Linear OOA(64¹⁵, 133183, F₆₄, 3, 5) (dual of [(133183, 3), 399534, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(64¹⁵, 133184, F₆₄, 2, 5) (dual of [(133184, 2), 266353, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
3. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
4. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
5. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
6. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
7. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
8. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
9. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
10. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
11. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
12. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
13. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
14. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
15. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
16. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
17. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
18. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
19. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
20. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
21. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
22. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
23. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
24. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
25. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
26. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
27. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
28. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
29. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
30. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
31. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
32. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
33. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
34. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
35. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
36. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
37. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
38. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
39. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
40. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
41. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
42. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
43. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
44. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
45. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
46. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
47. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
48. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
49. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
50. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
51. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
52. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
53. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
54. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
55. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
56. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
57. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
58. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
59. linear OOA(64⁰, 2081, F₆₄, 2, 0) (dual of [(2081, 2), 4162, 1]-NRT-code) (see above)
60. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
61. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code) (see above)
62. linear OOA(64¹, 2081, F₆₄, 2, 1) (dual of [(2081, 2), 4161, 2]-NRT-code) (see above)
63. linear OOA(64³, 2081, F₆₄, 2, 2) (dual of [(2081, 2), 4159, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64³, 4161, F₆₄, 2, 2) (dual of [(4161, 2), 8319, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(64³, 4161, F₆₄, 2) (dual of [4161, 4158, 3]-code), using
      - Hamming code H(3,64) [i]
64. linear OOA(64⁹, 2081, F₆₄, 2, 5) (dual of [(2081, 2), 4153, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
    2. linear OOA(64⁷, 2016, F₆₄, 2, 5) (dual of [(2016, 2), 4025, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(64⁷, 4032, F₆₄, 5) (dual of [4032, 4025, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁷, 4033, F₆₄, 5) (dual of [4033, 4026, 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(64⁵², 2929384, F₆₄, 3, 10) (dual of [(2929384, 3), 8788100, 11]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(64⁵⁶, 2929384, F₆₄, 3, 11) (dual of [(2929384, 3), 8788096, 12]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs