MinT - Information on Result #906828

Information on Result #906828

Linear OOA(32¹⁶, 33792, F₃₂, 2, 5) (dual of [(33792, 2), 67568, 6]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s, using
  - OOA with only one run / dual of NRT-code without redundancy [i]
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32⁰, 1056, F₃₂, 2, 0) (dual of [(1056, 2), 2112, 1]-NRT-code) (see above)
linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s, using
  - appending 1 arbitrary column [i] based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [i]
linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
linear OOA(32¹, 1056, F₃₂, 2, 1) (dual of [(1056, 2), 2111, 2]-NRT-code) (see above)
linear OOA(32³, 1056, F₃₂, 2, 2) (dual of [(1056, 2), 2109, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(32³, 1057, F₃₂, 2, 2) (dual of [(1057, 2), 2111, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
    - Hamming code H(3,32) [i]
linear OOA(32¹⁰, 1056, F₃₂, 2, 5) (dual of [(1056, 2), 2102, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32⁰, s, F₃₂, 2, 0) for arbitrarily large s (see above)
  2. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  3. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  4. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  5. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  6. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  7. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  8. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  9. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  10. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  11. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  12. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  13. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  14. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  15. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  16. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  17. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  18. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  19. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  20. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  21. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  22. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  23. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  24. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  25. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  26. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  27. linear OOA(32⁰, 33, F₃₂, 2, 0) (dual of [(33, 2), 66, 1]-NRT-code) (see above)
  28. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(32¹, s, F₃₂, 2, 1) for arbitrarily large s (see above)
  29. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
  30. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
  31. linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;64,32) [i]
  32. linear OOA(32⁵, 33, F₃₂, 2, 5) (dual of [(33, 2), 61, 6]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;61,32) [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(32⁶⁷, 4228093, F₃₂, 2, 11) (dual of [(4228093, 2), 8456119, 12]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(32⁶², 4228093, F₃₂, 2, 10) (dual of [(4228093, 2), 8456124, 11]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(32¹⁶, 33791, F₃₂, 6, 5) (dual of [(33791, 6), 202730, 6]-NRT-code)	[i]	OOA Stacking with Additional Row