MinT - Information on Result #2448760

Information on Result #2448760

Linear OOA(7⁵³, 42, F₇, 2, 28) (dual of [(42, 2), 31, 29]-NRT-code), using strength reduction based on linear OOA(7⁵³, 42, F₇, 2, 29) (dual of [(42, 2), 31, 30]-NRT-code), using

generalized (u,Â u+v)-construction [i] based on
1. linear OOA(7⁴, 6, F₇, 2, 4) (dual of [(6, 2), 8, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁴, 7, F₇, 2, 4) (dual of [(7, 2), 10, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;10,7) [i]
2. linear OOA(7⁴, 6, F₇, 2, 4) (dual of [(6, 2), 8, 5]-NRT-code) (see above)
3. linear OOA(7⁵, 6, F₇, 2, 5) (dual of [(6, 2), 7, 6]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁵, 7, F₇, 2, 5) (dual of [(7, 2), 9, 6]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;9,7) [i]
4. linear OOA(7⁷, 6, F₇, 2, 7) (dual of [(6, 2), 5, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁷, 7, F₇, 2, 7) (dual of [(7, 2), 7, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;7,7) [i]
5. linear OOA(7⁹, 6, F₇, 2, 9) (dual of [(6, 2), 3, 10]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁹, 7, F₇, 2, 9) (dual of [(7, 2), 5, 10]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;5,7) [i]
6. linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-NRT-code), using
  - complete OOA / dual of NRT-code with only one code word [i]
7. linear OOA(7¹², 6, F₇, 2, 12) (dual of [(6, 2), 0, 13]-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.