MinT - Information on Result #2664515

Information on Result #2664515

Linear OOA(7¹⁰², 44, F₇, 3, 60) (dual of [(44, 3), 30, 61]-NRT-code), using 2 step truncation based on linear OOA(7¹⁰⁴, 45, F₇, 3, 62) (dual of [(45, 3), 31, 63]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹³, 9, F₇, 3, 12) (dual of [(9, 3), 14, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 3, 12) (dual of [(13, 3), 26, 13]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
2. linear OOA(7¹⁶, 9, F₇, 3, 15) (dual of [(9, 3), 11, 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]
3. linear OOA(7²¹, 9, F₇, 3, 20) (dual of [(9, 3), 6, 21]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 21, 9)-net over F₇, using
    - net from sequence [i] based on digital (1, 8)-sequence over F₇ (see above)
4. linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7²⁷, 9, F₇, 3, 27) (dual of [(9, 3), 0, 28]-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.