MinT - Information on Result #906477

Information on Result #906477

Linear OOA(7¹⁰³, 63, F₇, 2, 62) (dual of [(63, 2), 23, 63]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7⁹, 9, F₇, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁹, 13, F₇, 2, 8) (dual of [(13, 2), 17, 9]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
    - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [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 (see above)
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.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.