MinT - Information on Result #1199494

Information on Result #1199494

Digital (80, 96, 1048839)-net over F₃₂, using net defined by OOA based on linear OOA(32⁹⁶, 1048839, F₃₂, 18, 16) (dual of [(1048839, 18), 18879006, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(32⁹⁶, 4195357, F₃₂, 2, 16) (dual of [(4195357, 2), 8390618, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32²⁰, 1056, F₃₂, 2, 8) (dual of [(1056, 2), 2092, 9]-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, using
        OOA with only one run / dual of NRT-code without redundancy [i]
      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(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, 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]
      26. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
      27. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
      28. linear OOA(32¹, 33, F₃₂, 2, 1) (dual of [(33, 2), 65, 2]-NRT-code) (see above)
      29. 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]
      30. linear OOA(32², 33, F₃₂, 2, 2) (dual of [(33, 2), 64, 3]-NRT-code) (see above)
      31. linear OOA(32⁴, 33, F₃₂, 2, 4) (dual of [(33, 2), 62, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;62,32) [i]
      32. linear OOA(32⁸, 33, F₃₂, 2, 8) (dual of [(33, 2), 58, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;58,32) [i]
  2. linear OOA(32⁷⁶, 4194301, F₃₂, 2, 16) (dual of [(4194301, 2), 8388526, 17]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(32⁷⁶, 8388602, F₃₂, 16) (dual of [8388602, 8388526, 17]-code), using
      - discarding factors / shortening the dual code based on linear OA(32⁷⁶, large, F₃₂, 16) (dual of [large, large−76, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 33554431Â = 32⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

None.