MinT - Information on Result #1129567

Information on Result #1129567

Linear OOA(3¹⁶¹, 66, F₃, 5, 77) (dual of [(66, 5), 169, 78]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(3⁵³, 28, F₃, 5, 38) (dual of [(28, 5), 87, 39]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(5;F,101P) [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]
linear OOA(3¹⁰⁸, 38, F₃, 5, 77) (dual of [(38, 5), 82, 78]-NRT-code), using
- constructionÂ X applied to AG(5;F,51P) âŠ‚ AG(5;F,54P) [i] based on
  1. linear OOA(3¹⁰³, 36, F₃, 5, 77) (dual of [(36, 5), 77, 78]-NRT-code), using algebraic-geometric NRT-code AG(5;F,51P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
  2. linear OOA(3⁹⁷, 36, F₃, 5, 71) (dual of [(36, 5), 83, 72]-NRT-code), using algebraic-geometric NRT-code AG(5;F,54P) with degPÂ =Â 2 [i] based on function field F/F₃ with g(F) = 26 and N(F) ≥ 36 (see above)
  3. linear OOA(3⁵, 2, F₃, 5, 5) (dual of [(2, 5), 5, 6]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(3⁵, 3, F₃, 5, 5) (dual of [(3, 5), 10, 6]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(5;10,3) [i]

Mode: Constructive and linear.

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