MinT - Information on Result #2664495

Information on Result #2664495

Linear OOA(7⁷⁷, 41, F₇, 3, 40) (dual of [(41, 3), 46, 41]-NRT-code), using 1 step truncation based on linear OOA(7⁷⁸, 42, F₇, 3, 41) (dual of [(42, 3), 48, 42]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁵, 6, F₇, 3, 5) (dual of [(6, 3), 13, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁵, 7, F₇, 3, 5) (dual of [(7, 3), 16, 6]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;16,7) [i]
2. linear OOA(7⁶, 6, F₇, 3, 6) (dual of [(6, 3), 12, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁶, 7, F₇, 3, 6) (dual of [(7, 3), 15, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;15,7) [i]
3. 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]
4. 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]
5. 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]
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.