MinT - Information on Result #906678

Information on Result #906678

Linear OOA(8²², 333, F₈, 2, 7) (dual of [(333, 2), 644, 8]-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(8⁵, 130, F₈, 2, 3) (dual of [(130, 2), 255, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
    - caps completed using a computer search [i]
linear OOA(8¹⁴, 130, F₈, 2, 7) (dual of [(130, 2), 246, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 7, 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]

Mode: Constructive and linear.

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