MinT - Information on Result #906905

Information on Result #906905

Linear OOA(49¹⁶, 120050, F₄₉, 2, 5) (dual of [(120050, 2), 240084, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 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]
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49⁰, 2450, F₄₉, 2, 0) (dual of [(2450, 2), 4900, 1]-NRT-code) (see above)
linear OOA(49¹, 2450, F₄₉, 2, 1) (dual of [(2450, 2), 4899, 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]
linear OOA(49¹, 2450, F₄₉, 2, 1) (dual of [(2450, 2), 4899, 2]-NRT-code) (see above)
linear OOA(49¹, 2450, F₄₉, 2, 1) (dual of [(2450, 2), 4899, 2]-NRT-code) (see above)
linear OOA(49³, 2450, F₄₉, 2, 2) (dual of [(2450, 2), 4897, 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]
linear OOA(49¹⁰, 2450, F₄₉, 2, 5) (dual of [(2450, 2), 4890, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(49⁰, s, F₄₉, 2, 0) for arbitrarily large s (see above)
  2. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  3. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  4. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  5. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  6. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  7. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  8. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  9. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  10. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  11. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  12. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  13. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  14. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  15. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  16. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  17. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  18. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  19. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  20. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  21. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  22. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  23. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  24. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  25. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  26. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  27. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  28. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  29. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  30. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  31. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  32. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  33. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  34. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  35. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  36. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  37. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  38. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  39. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  40. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  41. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  42. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  43. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  44. linear OOA(49⁰, 50, F₄₉, 2, 0) (dual of [(50, 2), 100, 1]-NRT-code) (see above)
  45. linear OOA(49¹, 50, F₄₉, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(49¹, s, F₄₉, 2, 1) for arbitrarily large s (see above)
  46. linear OOA(49¹, 50, F₄₉, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code) (see above)
  47. linear OOA(49¹, 50, F₄₉, 2, 1) (dual of [(50, 2), 99, 2]-NRT-code) (see above)
  48. 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]
  49. linear OOA(49⁵, 50, F₄₉, 2, 5) (dual of [(50, 2), 95, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;95,49) [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		Method
1	Linear OOA(49²³, 5882450, F₄₉, 2, 5) (dual of [(5882450, 2), 11764877, 6]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
2	Linear OOA(49¹⁶, 120049, F₄₉, 3, 5) (dual of [(120049, 3), 360131, 6]-NRT-code)	[i]	OOA Stacking with Additional Row
3	Linear OOA(49¹⁶, 120049, F₄₉, 6, 5) (dual of [(120049, 6), 720278, 6]-NRT-code)	[i]	OOA Stacking with Additional Row