MinT - Information on Result #2507153

Information on Result #2507153

Linear OOA(7¹⁰⁰, 57, F₇, 2, 68) (dual of [(57, 2), 14, 69]-NRT-code), using 7¹ times duplication based on linear OOA(7⁹⁹, 57, F₇, 2, 68) (dual of [(57, 2), 15, 69]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(7⁹⁷, 56, F₇, 2, 68) (dual of [(56, 2), 15, 69]-NRT-code), using
- strength reduction [i] based on linear OOA(7⁹⁷, 56, F₇, 2, 69) (dual of [(56, 2), 15, 70]-NRT-code), using
  - generalized (u,Â u+v)-construction [i] based on
    1. linear OOA(7⁹, 8, F₇, 2, 9) (dual of [(8, 2), 7, 10]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;7,7) [i]
    2. linear OOA(7¹¹, 8, F₇, 2, 11) (dual of [(8, 2), 5, 12]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;5,7) [i]
    3. linear OOA(7¹³, 8, F₇, 2, 13) (dual of [(8, 2), 3, 14]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,7) [i]
    4. 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]
    5. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
    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.