MinT - Information on Result #2806061

Information on Result #2806061

Linear OOA(3²²⁸, 78, F₃, 4, 112) (dual of [(78, 4), 84, 113]-NRT-code), using 3¹ times duplication based on linear OOA(3²²⁷, 78, F₃, 4, 112) (dual of [(78, 4), 85, 113]-NRT-code), using

strength reduction [i] based on linear OOA(3²²⁷, 78, F₃, 4, 113) (dual of [(78, 4), 85, 114]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(3⁵², 26, F₃, 4, 37) (dual of [(26, 4), 52, 38]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁵², 28, F₃, 4, 37) (dual of [(28, 4), 60, 38]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,74P) [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(3⁷¹, 26, F₃, 4, 56) (dual of [(26, 4), 33, 57]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁷¹, 28, F₃, 4, 56) (dual of [(28, 4), 41, 57]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(4;F,55P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28 (see above)
  3. linear OOA(3¹⁰⁴, 26, F₃, 4, 104) (dual of [(26, 4), 0, 105]-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.