MinT - Information on Result #2636234

Information on Result #2636234

Linear OOA(4²²⁶, 77, F₄, 3, 189) (dual of [(77, 3), 5, 190]-NRT-code), using strength reduction based on linear OOA(4²²⁶, 77, F₄, 3, 190) (dual of [(77, 3), 5, 191]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(4¹⁶, 7, F₄, 3, 15) (dual of [(7, 3), 5, 16]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4¹⁶, 9, F₄, 3, 15) (dual of [(9, 3), 11, 16]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,11P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
      - the Hermitian function field over F₄ [i]
2. linear OOA(4²⁰⁵, 70, F₄, 3, 174) (dual of [(70, 3), 5, 175]-NRT-code), using
  - repeating each code word 5 times [i] based on linear OOA(4³⁷, 14, F₄, 3, 34) (dual of [(14, 3), 5, 35]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [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.