MinT - Information on Result #1021925

Information on Result #1021925

Linear OOA(7⁶⁹, 36, F₇, 3, 37) (dual of [(36, 3), 39, 38]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7¹⁰, 9, F₇, 3, 9) (dual of [(9, 3), 17, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹⁰, 13, F₇, 3, 9) (dual of [(13, 3), 29, 10]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 10, 13)-net over F₇, using
    - 3 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7¹³, 9, F₇, 3, 12) (dual of [(9, 3), 14, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 3, 12) (dual of [(13, 3), 26, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇ (see above)
linear OOA(7¹⁹, 9, F₇, 3, 18) (dual of [(9, 3), 8, 19]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 19, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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