MinT - Information on Result #2518474

Information on Result #2518474

Linear OOA(27⁵⁸, large, F₂₇, 2, 4), using 27¹ times duplication based on linear OOA(27⁵⁷, large, F₂₇, 2, 4), using

17 times NRT-code embedding in larger space [i] based on linear OOA(27²³, large, F₂₇, 2, 4), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 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, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  3. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  4. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  5. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  6. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  7. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  8. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  9. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  10. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  11. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  12. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  13. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  14. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  15. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  16. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  17. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  18. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  19. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  20. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  21. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  22. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  23. linear OOA(27⁰, 551881, F₂₇, 2, 0) (dual of [(551881, 2), 1103762, 1]-NRT-code) (see above)
  24. linear OOA(27¹, 551881, F₂₇, 2, 1) (dual of [(551881, 2), 1103761, 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]
  25. linear OOA(27¹, 551881, F₂₇, 2, 1) (dual of [(551881, 2), 1103761, 2]-NRT-code) (see above)
  26. linear OOA(27⁵, 551881, F₂₇, 2, 2) (dual of [(551881, 2), 1103757, 3]-NRT-code), using
    - appending kth column [i] based on linear OA(27⁵, 551881, F₂₇, 2) (dual of [551881, 551876, 3]-code), using
      - Hamming code H(5,27) [i]
  27. linear OOA(27¹⁶, 4194301, F₂₇, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(27¹⁶, 8388602, F₂₇, 4) (dual of [8388602, 8388586, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(27¹⁶, large, F₂₇, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.