MinT - Information on Result #1020830

Information on Result #1020830

Linear OOA(3¹⁶³, 60, F₃, 3, 101) (dual of [(60, 3), 17, 102]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(3⁴⁴, 20, F₃, 3, 33) (dual of [(20, 3), 16, 34]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 44, 20)-net over F₃, using
  - net from sequence [i] based on digital (11, 19)-sequence over F₃, using
    - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₃ with g(F)Â =Â 9, N(F)Â =Â 19, and 1 place with degree 3 [i] based on function field F/F₃ with g(F) = 9 and N(F) ≥ 19, using an explicitly constructive algebraic function field [i]
linear OOA(3⁵⁹, 20, F₃, 3, 50) (dual of [(20, 3), 1, 51]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3⁵⁹, 21, F₃, 3, 50) (dual of [(21, 3), 4, 51]-NRT-code), using
  - repeating each code word 3 times [i] based on linear OOA(3¹⁷, 7, F₃, 3, 16) (dual of [(7, 3), 4, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
      - an explicitly constructive algebraic function field [i]
linear OOA(3⁶⁰, 20, F₃, 3, 60) (dual of [(20, 3), 0, 61]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

None.

None.