MinT - Information on Result #906483

Information on Result #906483

Linear OOA(7⁹⁸, 61, F₇, 2, 59) (dual of [(61, 2), 24, 60]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁸, 8, F₇, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;8,7) [i]
linear OOA(7⁹, 8, F₇, 2, 9) (dual of [(8, 2), 7, 10]-NRT-code), using
- extended Reedâ€“Solomon NRT-code RS_e(2;7,7) [i]
linear OOA(7¹², 9, F₇, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹², 13, F₇, 2, 11) (dual of [(13, 2), 14, 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, 2, 14) (dual of [(9, 2), 3, 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(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]
linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)

Mode: Constructive and linear.

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