MinT - Information on Result #906677

Information on Result #906677

Linear OOA(8²⁷, 333, F₈, 2, 8) (dual of [(333, 2), 639, 9]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
- appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
  - Hamming code H(3,8) [i]
linear OOA(8⁸, 130, F₈, 2, 4) (dual of [(130, 2), 252, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 4, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
      - Niederreiter sequence [i]
linear OOA(8¹⁶, 130, F₈, 2, 8) (dual of [(130, 2), 244, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 8, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)

Mode: Constructive and linear.

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