MinT - Information on Result #907003

Information on Result #907003

Linear OOA(64⁷⁵, 4198491, F₆₄, 2, 15) (dual of [(4198491, 2), 8396907, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(64¹⁸, 4190, F₆₄, 2, 7) (dual of [(4190, 2), 8362, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁰, s, F₆₄, 2, 0) for arbitrarily large s, using
      - OOA with only one run / dual of NRT-code without redundancy [i]
  2. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  3. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  4. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  5. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  6. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  7. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  8. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  9. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  10. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  11. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  12. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  13. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  14. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  15. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  16. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  17. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  18. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  19. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  20. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  21. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  22. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  23. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  24. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  25. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  26. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  27. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  28. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  29. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  30. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  31. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  32. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  33. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  34. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  35. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  36. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  37. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  38. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  39. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  40. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  41. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  42. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  43. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  44. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  45. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  46. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  47. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  48. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  49. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  50. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  51. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  52. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  53. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  54. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  55. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  56. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  57. linear OOA(64⁰, 65, F₆₄, 2, 0) (dual of [(65, 2), 130, 1]-NRT-code) (see above)
  58. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64¹, s, F₆₄, 2, 1) for arbitrarily large s, using
      - appending 1 arbitrary column [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]
  59. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
  60. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
  61. linear OOA(64¹, 65, F₆₄, 2, 1) (dual of [(65, 2), 129, 2]-NRT-code) (see above)
  62. linear OOA(64², 65, F₆₄, 2, 2) (dual of [(65, 2), 128, 3]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;128,64) [i]
  63. linear OOA(64⁴, 80, F₆₄, 2, 3) (dual of [(80, 2), 156, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(64⁴, 4097, F₆₄, 2, 3) (dual of [(4097, 2), 8190, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 64) [i]
  64. linear OOA(64⁸, 80, F₆₄, 2, 7) (dual of [(80, 2), 152, 8]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,152P) [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(64⁵⁷, 4194301, F₆₄, 2, 15) (dual of [(4194301, 2), 8388545, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(64⁵⁷, 8388602, F₆₄, 15) (dual of [8388602, 8388545, 16]-code), using
  - discarding factors / shortening the dual code based on linear OA(64⁵⁷, large, F₆₄, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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.