MinT - Information on Result #2489258

Information on Result #2489258

Linear OOA(3¹⁶¹, 170, F₃, 2, 51) (dual of [(170, 2), 179, 52]-NRT-code), using 3¹ times duplication based on linear OOA(3¹⁶⁰, 170, F₃, 2, 51) (dual of [(170, 2), 180, 52]-NRT-code), using

trace code [i] based on linear OOA(9⁸⁰, 85, F₉, 2, 51) (dual of [(85, 2), 90, 52]-NRT-code), using
- constructionÂ X applied to AG(2;F,94P) âŠ‚ AG(2;F,106P) [i] based on
  1. linear OOA(9⁶⁸, 73, F₉, 2, 51) (dual of [(73, 2), 78, 52]-NRT-code), using algebraic-geometric NRT-code AG(2;F,94P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]
  2. linear OOA(9⁵⁶, 73, F₉, 2, 39) (dual of [(73, 2), 90, 40]-NRT-code), using algebraic-geometric NRT-code AG(2;F,106P) [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74 (see above)
  3. linear OOA(9¹², 12, F₉, 2, 11) (dual of [(12, 2), 12, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(9¹², 16, F₉, 2, 11) (dual of [(16, 2), 20, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,20P) [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
        a function field by GarcÃa and Quoos [i]

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.