MinT - Information on Result #2642371

Information on Result #2642371

Linear OOA(7⁸⁹, 42, F₇, 3, 49) (dual of [(42, 3), 37, 50]-NRT-code), using strength reduction based on linear OOA(7⁸⁹, 42, F₇, 3, 50) (dual of [(42, 3), 37, 51]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁷, 6, F₇, 3, 7) (dual of [(6, 3), 11, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 3, 7) (dual of [(7, 3), 14, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;14,7) [i]
2. linear OOA(7⁸, 6, F₇, 3, 8) (dual of [(6, 3), 10, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁸, 7, F₇, 3, 8) (dual of [(7, 3), 13, 9]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;13,7) [i]
3. 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]
4. linear OOA(7¹², 6, F₇, 3, 12) (dual of [(6, 3), 6, 13]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹², 7, F₇, 3, 12) (dual of [(7, 3), 9, 13]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;9,7) [i]
5. 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]
6. 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]
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.