MinT - Information on Result #667725

Information on Result #667725

Linear OA(32¹⁶, 33792, F₃₂, 5) (dual of [33792, 33776, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32⁰, 1056, F₃₂, 0) (dual of [1056, 1056, 1]-code) (see above)
linear OA(32¹, 1056, F₃₂, 1) (dual of [1056, 1055, 2]-code), using
- discarding factors / shortening the dual code 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 OA(32¹, 1056, F₃₂, 1) (dual of [1056, 1055, 2]-code) (see above)
linear OA(32¹, 1056, F₃₂, 1) (dual of [1056, 1055, 2]-code) (see above)
linear OA(32³, 1056, F₃₂, 2) (dual of [1056, 1053, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(32³, 1057, F₃₂, 2) (dual of [1057, 1054, 3]-code), using
  - Hamming code H(3,32) [i]
linear OA(32¹⁰, 1056, F₃₂, 5) (dual of [1056, 1046, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
  2. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  3. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  4. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  5. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  6. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  7. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  8. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  9. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  10. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  11. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  12. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  13. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  14. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  15. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  16. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  17. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  18. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  19. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  20. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  21. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  22. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  23. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  24. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  25. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  26. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  27. linear OA(32⁰, 33, F₃₂, 0) (dual of [33, 33, 1]-code) (see above)
  28. linear OA(32¹, 33, F₃₂, 1) (dual of [33, 32, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(32¹, s, F₃₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
  29. linear OA(32¹, 33, F₃₂, 1) (dual of [33, 32, 2]-code) (see above)
  30. linear OA(32¹, 33, F₃₂, 1) (dual of [33, 32, 2]-code) (see above)
  31. linear OA(32², 33, F₃₂, 2) (dual of [33, 31, 3]-code or 33-arc in PG(1,32)), using
    - extended Reedâ€“Solomon code RS_e(31,32) [i]
    - Hamming code H(2,32) [i]
  32. linear OA(32⁵, 33, F₃₂, 5) (dual of [33, 28, 6]-code or 33-arc in PG(4,32)), using
    - extended Reedâ€“Solomon code RS_e(28,32) [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

None.