MinT - Information on Result #1022334

Information on Result #1022334

Linear OOA(64⁸⁴, 5600752, F₆₄, 3, 13) (dual of [(5600752, 3), 16802172, 14]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(64⁵, 4175, F₆₄, 3, 3) (dual of [(4175, 3), 12520, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(64⁵, 8264, F₆₄, 3, 3) (dual of [(8264, 3), 24787, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(64⁵, 8265, F₆₄, 3) (dual of [8265, 8260, 4]-code or 8265-cap in PG(4,64)), using
    - large caps in PG(4,Â b) [i]
linear OOA(64⁹, 4175, F₆₄, 3, 4) (dual of [(4175, 3), 12516, 5]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 3, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  58. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  59. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  60. linear OOA(64⁰, 65, F₆₄, 3, 0) (dual of [(65, 3), 195, 1]-NRT-code) (see above)
  61. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  62. linear OOA(64¹, 65, F₆₄, 3, 1) (dual of [(65, 3), 194, 2]-NRT-code) (see above)
  63. linear OOA(64², 65, F₆₄, 3, 2) (dual of [(65, 3), 193, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(3;193,64) [i]
  64. linear OOA(64⁵, 80, F₆₄, 3, 4) (dual of [(80, 3), 235, 5]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,235P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]
linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
  - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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.