MinT - Information on Result #909718

Information on Result #909718

Linear OOA(4⁸³, 44, F₄, 2, 64) (dual of [(44, 2), 5, 65]-NRT-code), using juxtaposition based on

linear OOA(4¹¹, 8, F₄, 2, 10) (dual of [(8, 2), 5, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹¹, 9, F₄, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,7P) [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(4⁶⁷, 36, F₄, 2, 53) (dual of [(36, 2), 5, 54]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
  2. linear OOA(4¹⁷, 9, F₄, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
    - dual of repetition NRT-code with length 9 [i]
  3. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  4. linear OOA(4¹⁸, 9, F₄, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

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