MinT - Information on Result #2449433

Information on Result #2449433

Linear OOA(7¹⁰⁷, 63, F₇, 2, 68) (dual of [(63, 2), 19, 69]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁷, 63, F₇, 2, 69) (dual of [(63, 2), 19, 70]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹⁰, 9, F₇, 2, 9) (dual of [(9, 2), 8, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹⁰, 13, F₇, 2, 9) (dual of [(13, 2), 16, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 10, 13)-net over F₇, using
      - 3 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
2. 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)
3. linear OOA(7¹⁴, 9, F₇, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 14, 9)-net over F₇, using
    - net from sequence [i] based on digital (1, 8)-sequence over F₇, using
      - Niederreiter sequence [i]
4. 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]
5. 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]
6. linear OOA(7¹⁸, 9, F₇, 2, 18) (dual of [(9, 2), 0, 19]-NRT-code) (see above)
7. 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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7¹⁰⁵, 62, F₇, 2, 66) (dual of [(62, 2), 19, 67]-NRT-code)	[i]		Truncation for OOAs