MinT - Information on Result #2806167

Information on Result #2806167

Linear OOA(3²⁵⁰, 85, F₃, 4, 124) (dual of [(85, 4), 90, 125]-NRT-code), using 3¹ times duplication based on linear OOA(3²⁴⁹, 85, F₃, 4, 124) (dual of [(85, 4), 91, 125]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(3²⁴⁵, 84, F₃, 4, 124) (dual of [(84, 4), 91, 125]-NRT-code), using
- strength reduction [i] based on linear OOA(3²⁴⁵, 84, F₃, 4, 125) (dual of [(84, 4), 91, 126]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(3⁵⁶, 28, F₃, 4, 41) (dual of [(28, 4), 56, 42]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,70P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(3⁷⁷, 28, F₃, 4, 62) (dual of [(28, 4), 35, 63]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,49P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
    3. linear OOA(3¹¹², 28, F₃, 4, 112) (dual of [(28, 4), 0, 113]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [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.