MinT - Information on Result #2642729

Information on Result #2642729

Linear OOA(7¹⁰⁶, 42, F₇, 3, 68) (dual of [(42, 3), 20, 69]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁶, 42, F₇, 3, 71) (dual of [(42, 3), 20, 72]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹⁰, 6, F₇, 3, 10) (dual of [(6, 3), 8, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹⁰, 7, F₇, 3, 10) (dual of [(7, 3), 11, 11]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;11,7) [i]
2. linear OOA(7¹¹, 6, F₇, 3, 11) (dual of [(6, 3), 7, 12]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹¹, 7, F₇, 3, 11) (dual of [(7, 3), 10, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;10,7) [i]
3. linear OOA(7¹⁴, 6, F₇, 3, 14) (dual of [(6, 3), 4, 15]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹⁴, 7, F₇, 3, 14) (dual of [(7, 3), 7, 15]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;7,7) [i]
4. linear OOA(7¹⁷, 6, F₇, 3, 17) (dual of [(6, 3), 1, 18]-NRT-code), using
  - dual of repetition NRT-code with length 6 [i]
5. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
6. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 0, 19]-NRT-code) (see above)
7. linear OOA(7¹⁸, 6, F₇, 3, 18) (dual of [(6, 3), 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.