MinT - Information on Result #2642648

Information on Result #2642648

Linear OOA(7¹⁰³, 42, F₇, 3, 66) (dual of [(42, 3), 23, 67]-NRT-code), using strength reduction based on linear OOA(7¹⁰³, 42, F₇, 3, 67) (dual of [(42, 3), 23, 68]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁹, 6, F₇, 3, 9) (dual of [(6, 3), 9, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁹, 7, F₇, 3, 9) (dual of [(7, 3), 12, 10]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;12,7) [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(7¹³, 6, F₇, 3, 13) (dual of [(6, 3), 5, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹³, 7, F₇, 3, 13) (dual of [(7, 3), 8, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,7) [i]
4. linear OOA(7¹⁶, 6, F₇, 3, 16) (dual of [(6, 3), 2, 17]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹⁶, 7, F₇, 3, 16) (dual of [(7, 3), 5, 17]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;5,7) [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.