MinT - Information on Result #2507067

Information on Result #2507067

Linear OOA(7⁸⁷, 57, F₇, 2, 50) (dual of [(57, 2), 27, 51]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(7⁸⁵, 56, F₇, 2, 50) (dual of [(56, 2), 27, 51]-NRT-code), using

strength reduction [i] based on linear OOA(7⁸⁵, 56, F₇, 2, 51) (dual of [(56, 2), 27, 52]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁷, 8, F₇, 2, 7) (dual of [(8, 2), 9, 8]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;9,7) [i]
  2. linear OOA(7⁸, 8, F₇, 2, 8) (dual of [(8, 2), 8, 9]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;8,7) [i]
  3. linear OOA(7¹⁰, 8, F₇, 2, 10) (dual of [(8, 2), 6, 11]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;6,7) [i]
  4. linear OOA(7¹², 8, F₇, 2, 12) (dual of [(8, 2), 4, 13]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;4,7) [i]
  5. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code), using
    - complete OOA / dual of NRT-code with only one code word [i]
  6. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
  7. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-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.