MinT - Information on Result #2449473

Information on Result #2449473

Linear OOA(7¹⁰⁹, 60, F₇, 2, 76) (dual of [(60, 2), 11, 77]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁹, 60, F₇, 2, 77) (dual of [(60, 2), 11, 78]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹³, 10, F₇, 2, 12) (dual of [(10, 2), 7, 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, using
      - a shift-net [i]
2. linear OOA(7¹⁷, 10, F₇, 2, 15) (dual of [(10, 2), 3, 16]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(7¹⁷, 20, F₇, 15) (dual of [20, 3, 16]-code), using
    - 2 times truncation [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]
3. linear OOA(7¹⁹, 10, F₇, 2, 19) (dual of [(10, 2), 1, 20]-NRT-code), using
  - dual of repetition NRT-code with length 10 [i]
4. linear OOA(7²⁰, 10, F₇, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
5. linear OOA(7²⁰, 10, F₇, 2, 20) (dual of [(10, 2), 0, 21]-NRT-code) (see above)
6. linear OOA(7²⁰, 10, F₇, 2, 20) (dual of [(10, 2), 0, 21]-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.