MinT - Information on Result #1064221

Information on Result #1064221

Linear OOA(3¹⁷⁸, 85, F₃, 4, 60) (dual of [(85, 4), 162, 61]-NRT-code), using OOA 2-folding based on linear OOA(3¹⁷⁸, 170, F₃, 2, 60) (dual of [(170, 2), 162, 61]-NRT-code), using

trace code [i] based on linear OOA(9⁸⁹, 85, F₉, 2, 60) (dual of [(85, 2), 81, 61]-NRT-code), using
- constructionÂ X applied to AG(2;F,85P) âŠ‚ AG(2;F,97P) [i] based on
  1. linear OOA(9⁷⁷, 73, F₉, 2, 60) (dual of [(73, 2), 69, 61]-NRT-code), using algebraic-geometric NRT-code AG(2;F,85P) [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(9⁶⁵, 73, F₉, 2, 48) (dual of [(73, 2), 81, 49]-NRT-code), using algebraic-geometric NRT-code AG(2;F,97P) [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.