MinT - Information on Result #910111

Information on Result #910111

Linear OOA(7¹⁰⁹, 58, F₇, 2, 84) (dual of [(58, 2), 7, 85]-NRT-code), using juxtaposition based on

linear OOA(7¹³, 10, F₇, 2, 12) (dual of [(10, 2), 7, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹³, 13, F₇, 2, 12) (dual of [(13, 2), 13, 13]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 13, 13)-net over F₇, using
    - a shift-net [i]
linear OOA(7⁸⁹, 48, F₇, 2, 71) (dual of [(48, 2), 7, 72]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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]
  2. linear OOA(7¹⁴, 8, F₇, 2, 14) (dual of [(8, 2), 2, 15]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;2,7) [i]
  3. 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]
  4. linear OOA(7¹⁶, 8, F₇, 2, 16) (dual of [(8, 2), 0, 17]-NRT-code) (see above)
  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)

Mode: Constructive and linear.

None.

The following results depend on this result: