MinT - Information on Result #2642585

Information on Result #2642585

Linear OOA(7¹⁰⁰, 42, F₇, 3, 60) (dual of [(42, 3), 26, 61]-NRT-code), using strength reduction based on linear OOA(7¹⁰⁰, 42, F₇, 3, 63) (dual of [(42, 3), 26, 64]-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(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]
3. 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]
4. linear OOA(7¹⁵, 6, F₇, 3, 15) (dual of [(6, 3), 3, 16]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7¹⁵, 7, F₇, 3, 15) (dual of [(7, 3), 6, 16]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;6,7) [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.