MinT - Information on Result #909743

Information on Result #909743

Linear OOA(4²⁵³, 129, F₄, 2, 192) (dual of [(129, 2), 5, 193]-NRT-code), using juxtaposition based on

linear OOA(4¹³, 9, F₄, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
  - the Hermitian function field over F₄ [i]
linear OOA(4²³⁵, 120, F₄, 2, 179) (dual of [(120, 2), 5, 180]-NRT-code), using
- repeating each code word 3 times [i] based on linear OOA(4⁷⁵, 40, F₄, 2, 59) (dual of [(40, 2), 5, 60]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(4¹⁶, 10, F₄, 2, 14) (dual of [(10, 2), 4, 15]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,5P) [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
        an explicitly constructive algebraic function field [i]
    2. linear OOA(4¹⁹, 10, F₄, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
      - dual of repetition NRT-code with length 10 [i]
    3. linear OOA(4²⁰, 10, F₄, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
      - complete OOA / dual of NRT-code with only one code word [i]
    4. linear OOA(4²⁰, 10, F₄, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)

Mode: Constructive and linear.

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