MinT - Information on Result #906804

Information on Result #906804

Linear OOA(27⁶⁷, 4214713, F₂₇, 2, 11) (dual of [(4214713, 2), 8429359, 12]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(27¹⁶, 20412, F₂₇, 2, 5) (dual of [(20412, 2), 40808, 6]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  3. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  4. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  5. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  6. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  7. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  8. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  9. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  10. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  11. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  12. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  13. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  14. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  15. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  16. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  17. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  18. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  19. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  20. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  21. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  22. linear OOA(27⁰, 756, F₂₇, 2, 0) (dual of [(756, 2), 1512, 1]-NRT-code) (see above)
  23. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [i] based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  24. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code) (see above)
  25. linear OOA(27¹, 756, F₂₇, 2, 1) (dual of [(756, 2), 1511, 2]-NRT-code) (see above)
  26. linear OOA(27³, 756, F₂₇, 2, 2) (dual of [(756, 2), 1509, 3]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27³, 757, F₂₇, 2, 2) (dual of [(757, 2), 1511, 3]-NRT-code), using
      - appending kth column [i] based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
        Hamming code H(3,27) [i]
  27. linear OOA(27¹⁰, 756, F₂₇, 2, 5) (dual of [(756, 2), 1502, 6]-NRT-code), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27⁰, s, F₂₇, 2, 0) for arbitrarily large s (see above)
      2. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      3. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      4. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      5. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      6. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      7. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      8. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      9. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      10. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      11. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      12. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      13. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      14. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      15. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      16. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      17. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      18. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      19. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      20. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      21. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      22. linear OOA(27⁰, 28, F₂₇, 2, 0) (dual of [(28, 2), 56, 1]-NRT-code) (see above)
      23. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(27¹, s, F₂₇, 2, 1) for arbitrarily large s (see above)
      24. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      25. linear OOA(27¹, 28, F₂₇, 2, 1) (dual of [(28, 2), 55, 2]-NRT-code) (see above)
      26. linear OOA(27², 28, F₂₇, 2, 2) (dual of [(28, 2), 54, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;54,27) [i]
      27. linear OOA(27⁵, 28, F₂₇, 2, 5) (dual of [(28, 2), 51, 6]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;51,27) [i]
linear OOA(27⁵¹, 4194301, F₂₇, 2, 11) (dual of [(4194301, 2), 8388551, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(27⁵¹, 8388602, F₂₇, 11) (dual of [8388602, 8388551, 12]-code), using
  - discarding factors / shortening the dual code based on linear OA(27⁵¹, large, F₂₇, 11) (dual of [large, large−51, 12]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [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.

Other Results with Identical Parameters

None.

Depending Results

None.