MinT - Information on Result #906473

Information on Result #906473

Linear OOA(7¹⁰³, 62, F₇, 2, 63) (dual of [(62, 2), 21, 64]-NRT-code), using generalized (u,Â u+v)-construction based on

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(7¹¹, 9, F₇, 2, 10) (dual of [(9, 2), 7, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹¹, 13, F₇, 2, 10) (dual of [(13, 2), 15, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 11, 13)-net over F₇, using
    - 2 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7¹³, 9, F₇, 2, 12) (dual of [(9, 2), 5, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇ (see above)
linear OOA(7¹⁶, 9, F₇, 2, 15) (dual of [(9, 2), 2, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 16, 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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