MinT - Information on Result #909530

Information on Result #909530

Linear OOA(4²³⁸, 123, F₄, 2, 170) (dual of [(123, 2), 8, 171]-NRT-code), using juxtaposition based on

linear OOA(4²², 15, F₄, 2, 18) (dual of [(15, 2), 8, 19]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,11P) [i] based on function field F/F₄ with g(F) = 4 and N(F) ≥ 15, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4²⁰⁸, 108, F₄, 2, 151) (dual of [(108, 2), 8, 152]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁴⁷, 27, F₄, 2, 37) (dual of [(27, 2), 7, 38]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,16P) [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]
  2. linear OOA(4⁵³, 27, F₄, 2, 50) (dual of [(27, 2), 1, 51]-NRT-code), using
    - strength reduction [i] based on linear OOA(4⁵³, 27, F₄, 2, 53) (dual of [(27, 2), 1, 54]-NRT-code), using
      - dual of repetition NRT-code with length 27 [i]
  3. linear OOA(4⁵⁴, 27, F₄, 2, 54) (dual of [(27, 2), 0, 55]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4⁵⁴, 27, F₄, 2, 54) (dual of [(27, 2), 0, 55]-NRT-code) (see above)

Mode: Constructive and linear.

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