MinT - Information on Result #2507087

Information on Result #2507087

Linear OOA(7⁸³, 50, F₇, 2, 53) (dual of [(50, 2), 17, 54]-NRT-code), using 7¹ times duplication based on linear OOA(7⁸², 50, F₇, 2, 53) (dual of [(50, 2), 18, 54]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(7⁸⁰, 49, F₇, 2, 53) (dual of [(49, 2), 18, 54]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(7⁸, 7, F₇, 2, 8) (dual of [(7, 2), 6, 9]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;6,7) [i]
  3. linear OOA(7¹⁰, 7, F₇, 2, 10) (dual of [(7, 2), 4, 11]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;4,7) [i]
  4. linear OOA(7¹³, 7, F₇, 2, 13) (dual of [(7, 2), 1, 14]-NRT-code), using
    - dual of repetition NRT-code with length 7 [i]
    - Reedâ€“Solomon NRT-code RS(2;1,7) [i]
  5. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  6. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
  7. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-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.