MinT - Information on Result #1049601

Information on Result #1049601

Linear OOA(4²⁵⁷, 91, F₄, 3, 190) (dual of [(91, 3), 16, 191]-NRT-code), using juxtaposition based on

linear OOA(4⁸³, 33, F₄, 3, 68) (dual of [(33, 3), 16, 69]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,30P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]
linear OOA(4¹⁵⁸, 58, F₄, 3, 121) (dual of [(58, 3), 16, 122]-NRT-code), using
- constructionÂ X applied to AG(3;F,43P) âŠ‚ AG(3;F,48P) [i] based on
  1. linear OOA(4¹⁵⁴, 55, F₄, 3, 121) (dual of [(55, 3), 11, 122]-NRT-code), using algebraic-geometric NRT-code AG(3;F,43P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]
  2. linear OOA(4¹⁴⁹, 55, F₄, 3, 116) (dual of [(55, 3), 16, 117]-NRT-code), using algebraic-geometric NRT-code AG(3;F,48P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁴, 3, F₄, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4⁴, 4, F₄, 3, 4) (dual of [(4, 3), 8, 5]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;8,4) [i]

Mode: Constructive and linear.

None.

The following results depend on this result: