MinT - Information on Result #2698109

Information on Result #2698109

Linear OOA(7¹⁰⁰, 50, F₇, 3, 52) (dual of [(50, 3), 50, 53]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(7⁹⁷, 49, F₇, 3, 52) (dual of [(49, 3), 50, 53]-NRT-code), using

strength reduction [i] based on linear OOA(7⁹⁷, 49, F₇, 3, 53) (dual of [(49, 3), 50, 54]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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, 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, 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(7¹³, 7, F₇, 3, 13) (dual of [(7, 3), 8, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;8,7) [i]
  5. linear OOA(7¹⁷, 7, F₇, 3, 17) (dual of [(7, 3), 4, 18]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;4,7) [i]
  6. linear OOA(7²¹, 7, F₇, 3, 21) (dual of [(7, 3), 0, 22]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  7. linear OOA(7²¹, 7, F₇, 3, 21) (dual of [(7, 3), 0, 22]-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.