MinT - Information on Result #1049606

Information on Result #1049606

Linear OOA(4²⁵⁹, 91, F₄, 3, 194) (dual of [(91, 3), 14, 195]-NRT-code), using juxtaposition based on

linear OOA(4⁸⁵, 33, F₄, 3, 70) (dual of [(33, 3), 14, 71]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,28P) [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(4¹⁶⁰, 58, F₄, 3, 123) (dual of [(58, 3), 14, 124]-NRT-code), using
- constructionÂ X applied to AG(3;F,41P) âŠ‚ AG(3;F,46P) [i] based on
  1. linear OOA(4¹⁵⁶, 55, F₄, 3, 123) (dual of [(55, 3), 9, 124]-NRT-code), using algebraic-geometric NRT-code AG(3;F,41P) [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(4¹⁵¹, 55, F₄, 3, 118) (dual of [(55, 3), 14, 119]-NRT-code), using algebraic-geometric NRT-code AG(3;F,46P) [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.

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