MinT - Information on Result #910110

Information on Result #910110

Linear OOA(7¹⁰⁹, 59, F₇, 2, 80) (dual of [(59, 2), 9, 81]-NRT-code), using juxtaposition based on

linear OOA(7¹¹, 10, F₇, 2, 10) (dual of [(10, 2), 9, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7¹¹, 13, F₇, 2, 10) (dual of [(13, 2), 15, 11]-NRT-code), using
  - extracting embedded OOA [i] based on digital (1, 11, 13)-net over F₇, using
    - 2 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
      - a shift-net [i]
linear OOA(7⁸⁹, 49, F₇, 2, 69) (dual of [(49, 2), 9, 70]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(7⁹, 7, F₇, 2, 9) (dual of [(7, 2), 5, 10]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;5,7) [i]
  2. linear OOA(7¹¹, 7, F₇, 2, 11) (dual of [(7, 2), 3, 12]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;3,7) [i]
  3. 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]
  4. 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]
  5. linear OOA(7¹⁴, 7, F₇, 2, 14) (dual of [(7, 2), 0, 15]-NRT-code) (see above)
  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.

None.

The following results depend on this result: