MinT - Information on Result #2475391

Information on Result #2475391

Linear OOA(7⁶¹, 43, F₇, 2, 34) (dual of [(43, 2), 25, 35]-NRT-code), using 1 step truncation based on linear OOA(7⁶², 44, F₇, 2, 35) (dual of [(44, 2), 26, 36]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁹, 11, F₇, 2, 8) (dual of [(11, 2), 13, 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]
2. linear OOA(7¹², 11, F₇, 2, 11) (dual of [(11, 2), 10, 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)
3. linear OOA(7¹⁹, 11, F₇, 2, 17) (dual of [(11, 2), 3, 18]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(7¹⁹, 22, F₇, 17) (dual of [22, 3, 18]-code), using
    - a projective code based on a Barlotti arc [i]
4. linear OOA(7²², 11, F₇, 2, 22) (dual of [(11, 2), 0, 23]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]

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.