MinT - Information on Result #1129259

Information on Result #1129259

Linear OOA(3²²⁹, 77, F₃, 5, 110) (dual of [(77, 5), 156, 111]-NRT-code), using constructionÂ X based on

linear OOA(3²¹⁶, 72, F₃, 5, 110) (dual of [(72, 5), 144, 111]-NRT-code), using OOA from sequence [i] based on digital (106, 72)-sequence over F₃, using
- base reduction for sequences [i] based on digital (17, 72)-sequence over F₉, using
  - s-reduction based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]
linear OOA(3²⁰³, 72, F₃, 5, 97) (dual of [(72, 5), 157, 98]-NRT-code), using OOA from sequence [i] based on digital (106, 72)-sequence over F₃ (see above)
linear OOA(3¹³, 5, F₃, 5, 12) (dual of [(5, 5), 12, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹³, 7, F₃, 5, 12) (dual of [(7, 5), 22, 13]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,22P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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