Information on Result #733644

Linear OA(3215, 32864, F32, 5) (dual of [32864, 32849, 6]-code), using generalized (u, u+v)-construction based on
  1. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code), using
  2. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  3. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  4. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  5. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  6. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  7. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  8. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  9. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  10. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  11. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  12. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  13. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  14. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  15. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  16. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  17. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  18. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  19. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  20. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  21. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  22. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  23. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  24. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  25. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  26. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  27. linear OA(320, 1027, F32, 0) (dual of [1027, 1027, 1]-code) (see above)
  28. linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code), using
  29. linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code) (see above)
  30. linear OA(321, 1027, F32, 1) (dual of [1027, 1026, 2]-code) (see above)
  31. linear OA(323, 1027, F32, 2) (dual of [1027, 1024, 3]-code), using
  32. linear OA(329, 1027, F32, 5) (dual of [1027, 1018, 6]-code), using
    • construction XX applied to C1 = C([1022,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([1022,3]) [i] based on
      1. linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
      2. linear OA(327, 1023, F32, 4) (dual of [1023, 1016, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
      3. linear OA(329, 1023, F32, 5) (dual of [1023, 1014, 6]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
      4. linear OA(325, 1023, F32, 3) (dual of [1023, 1018, 4]-code or 1023-cap in PG(4,32)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
      5. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)

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:

ResultThis
result
only		Method
1Linear OOA(3215, 32864, F32, 2, 5) (dual of [(32864, 2), 65713, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Digital (10, 15, 32864)-net over F32 [i]
3Linear OOA(3215, 16432, F32, 2, 5) (dual of [(16432, 2), 32849, 6]-NRT-code) [i]OOA Folding