MinT - Information on Result #2637570

Information on Result #2637570

Linear OOA(4²⁴², 121, F₄, 3, 138) (dual of [(121, 3), 121, 139]-NRT-code), using strength reduction based on linear OOA(4²⁴², 121, F₄, 3, 139) (dual of [(121, 3), 121, 140]-NRT-code), using

constructionÂ X applied to AG(3;F,169P) âŠ‚ AG(3;F,193P) [i] based on
1. linear OOA(4²¹², 103, F₄, 3, 139) (dual of [(103, 3), 97, 140]-NRT-code), using algebraic-geometric NRT-code AG(3;F,169P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
  - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
2. linear OOA(4¹⁸⁸, 103, F₄, 3, 115) (dual of [(103, 3), 121, 116]-NRT-code), using algebraic-geometric NRT-code AG(3;F,193P) [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104 (see above)
3. linear OOA(4³⁰, 18, F₄, 3, 23) (dual of [(18, 3), 24, 24]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(4³⁰, 21, F₄, 3, 23) (dual of [(21, 3), 33, 24]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,39P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, using
      - an explicitly constructive algebraic function field [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.