MinT - Information on Result #666493

Information on Result #666493

Linear OA(27¹⁶, 20412, F₂₇, 5) (dual of [20412, 20396, 6]-code), using generalized (u,Â u+v)-construction based on

linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27⁰, 756, F₂₇, 0) (dual of [756, 756, 1]-code) (see above)
linear OA(27¹, 756, F₂₇, 1) (dual of [756, 755, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]
linear OA(27¹, 756, F₂₇, 1) (dual of [756, 755, 2]-code) (see above)
linear OA(27¹, 756, F₂₇, 1) (dual of [756, 755, 2]-code) (see above)
linear OA(27³, 756, F₂₇, 2) (dual of [756, 753, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(27³, 757, F₂₇, 2) (dual of [757, 754, 3]-code), using
  - Hamming code H(3,27) [i]
linear OA(27¹⁰, 756, F₂₇, 5) (dual of [756, 746, 6]-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s (see above)
  2. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  3. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  4. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  5. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  6. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  7. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  8. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  9. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  10. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  11. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  12. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  13. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  14. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  15. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  16. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  17. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  18. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  19. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  20. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  21. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  22. linear OA(27⁰, 28, F₂₇, 0) (dual of [28, 28, 1]-code) (see above)
  23. linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s (see above)
  24. linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code) (see above)
  25. linear OA(27¹, 28, F₂₇, 1) (dual of [28, 27, 2]-code) (see above)
  26. linear OA(27², 28, F₂₇, 2) (dual of [28, 26, 3]-code or 28-arc in PG(1,27)), using
    - extended Reedâ€“Solomon code RS_e(26,27) [i]
    - Hamming code H(2,27) [i]
  27. linear OA(27⁵, 28, F₂₇, 5) (dual of [28, 23, 6]-code or 28-arc in PG(4,27)), using
    - extended Reedâ€“Solomon code RS_e(23,27) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 28Â | 27²âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [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.