MinT - Information on Result #1021857

Information on Result #1021857

Linear OOA(7⁸⁵, 44, F₇, 3, 44) (dual of [(44, 3), 47, 45]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁸, 8, F₇, 3, 8) (dual of [(8, 3), 16, 9]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(3;16,7) [i]
linear OOA(7¹², 9, F₇, 3, 11) (dual of [(9, 3), 15, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹², 13, F₇, 3, 11) (dual of [(13, 3), 27, 12]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 12, 13)-net over F₇, using
    - 1 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7¹⁵, 9, F₇, 3, 14) (dual of [(9, 3), 12, 15]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 15, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
    - Niederreiter sequence [i]
linear OOA(7²³, 9, F₇, 3, 22) (dual of [(9, 3), 4, 23]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 23, 9)-net over F₇, using
  - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
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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