MinT - Information on Result #2642082

Information on Result #2642082

Linear OOA(7⁶⁸, 25, F₇, 3, 53) (dual of [(25, 3), 7, 54]-NRT-code), using strength reduction based on linear OOA(7⁶⁸, 25, F₇, 3, 54) (dual of [(25, 3), 7, 55]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7¹⁰, 5, F₇, 3, 10) (dual of [(5, 3), 5, 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(7¹³, 5, F₇, 3, 13) (dual of [(5, 3), 2, 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]
3. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
4. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-NRT-code) (see above)
5. linear OOA(7¹⁵, 5, F₇, 3, 15) (dual of [(5, 3), 0, 16]-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.