MinT - Information on Result #944789

Information on Result #944789

Linear OOA(49¹⁵, 60073, F₄₉, 3, 5) (dual of [(60073, 3), 180204, 6]-NRT-code), using OOA stacking with additional row based on linear OOA(49¹⁵, 60074, F₄₉, 2, 5) (dual of [(60074, 2), 120133, 6]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 2, 0) for arbitrarily large s, using
    - OOA with only one run / dual of NRT-code without redundancy [i]
2. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
3. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
4. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
5. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
6. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
7. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
8. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
9. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
10. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
11. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
12. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
13. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
14. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
15. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
16. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
17. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
18. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
19. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
20. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
21. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
22. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
23. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
24. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
25. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
26. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
27. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
28. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
29. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
30. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
31. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
32. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
33. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
34. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
35. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
36. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
37. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
38. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
39. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
40. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
41. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
42. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
43. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
44. linear OOA(49⁰, 1226, F₄₉, 2, 0) (dual of [(1226, 2), 2452, 1]-NRT-code) (see above)
45. linear OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 2, 1) for arbitrarily large s, using
    - appending 1 arbitrary column [i] based on linear OA(49¹, s, F₄₉, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
46. linear OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code) (see above)
47. linear OOA(49¹, 1226, F₄₉, 2, 1) (dual of [(1226, 2), 2451, 2]-NRT-code) (see above)
48. linear OOA(49³, 1226, F₄₉, 2, 2) (dual of [(1226, 2), 2449, 3]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(49³, 2451, F₄₉, 2, 2) (dual of [(2451, 2), 4899, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(49³, 2451, F₄₉, 2) (dual of [2451, 2448, 3]-code), using
      - Hamming code H(3,49) [i]
49. linear OOA(49⁹, 1226, F₄₉, 2, 5) (dual of [(1226, 2), 2443, 6]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(49², 50, F₄₉, 2, 2) (dual of [(50, 2), 98, 3]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;98,49) [i]
    2. linear OOA(49⁷, 1176, F₄₉, 2, 5) (dual of [(1176, 2), 2345, 6]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(49⁷, 2352, F₄₉, 5) (dual of [2352, 2345, 6]-code), using
        discarding factors / shortening the dual code based on linear OA(49⁷, 2353, F₄₉, 5) (dual of [2353, 2346, 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

None.