MinT - Information on Result #1129382

Information on Result #1129382

Linear OOA(3²³⁶, 78, F₃, 5, 116) (dual of [(78, 5), 154, 117]-NRT-code), using constructionÂ X based on

linear OOA(3²²³, 73, F₃, 5, 116) (dual of [(73, 5), 142, 117]-NRT-code), using OOA from sequence [i] based on digital (107, 73)-sequence over F₃, using
- base reduction for sequences [i] 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(3²¹⁰, 73, F₃, 5, 103) (dual of [(73, 5), 155, 104]-NRT-code), using OOA from sequence [i] based on digital (107, 73)-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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