MinT - Information on Result #906460

Information on Result #906460

Linear OOA(7¹⁰⁹, 63, F₇, 2, 71) (dual of [(63, 2), 17, 72]-NRT-code), using generalized (u,Â u+v)-construction based on

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(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 (see above)
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(7¹⁷, 9, F₇, 2, 17) (dual of [(9, 2), 1, 18]-NRT-code), using
- dual of repetition NRT-code with length 9 [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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