MinT - Information on Result #1488681

Information on Result #1488681

Linear OOA(7¹⁰⁷, 52, F₇, 3, 65) (dual of [(52, 3), 49, 66]-NRT-code), using OOA 2-folding based on linear OOA(7¹⁰⁷, 104, F₇, 2, 65) (dual of [(104, 2), 101, 66]-NRT-code), using

constructionÂ X applied to AG(2;F,124P) âŠ‚ AG(2;F,133P) [i] based on
1. linear OOA(7⁹⁸, 95, F₇, 2, 65) (dual of [(95, 2), 92, 66]-NRT-code), using algebraic-geometric NRT-code AG(2;F,124P) [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96, using
  - an algebraic function field by Teo [i]
2. linear OOA(7⁸⁹, 95, F₇, 2, 56) (dual of [(95, 2), 101, 57]-NRT-code), using algebraic-geometric NRT-code AG(2;F,133P) [i] based on function field F/F₇ with g(F) = 33 and N(F) ≥ 96 (see above)
3. linear OOA(7⁹, 9, F₇, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(7⁹, 13, F₇, 2, 8) (dual of [(13, 2), 17, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 9, 13)-net over F₇, using
      - 4 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]

Mode: 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.