MinT - Information on Result #1049591

Information on Result #1049591

Linear OOA(4²⁵⁷, 92, F₄, 3, 185) (dual of [(92, 3), 19, 186]-NRT-code), using juxtaposition based on

linear OOA(4⁸⁰, 33, F₄, 3, 65) (dual of [(33, 3), 19, 66]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,33P) [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, 59, F₄, 3, 119) (dual of [(59, 3), 19, 120]-NRT-code), using
- constructionÂ X applied to AG(3;F,45P) âŠ‚ AG(3;F,52P) [i] based on
  1. linear OOA(4¹⁵², 55, F₄, 3, 119) (dual of [(55, 3), 13, 120]-NRT-code), using algebraic-geometric NRT-code AG(3;F,45P) [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(4¹⁴⁵, 55, F₄, 3, 112) (dual of [(55, 3), 20, 113]-NRT-code), using algebraic-geometric NRT-code AG(3;F,52P) [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56 (see above)
  3. linear OOA(4⁶, 4, F₄, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;6,4) [i]

Mode: Constructive and linear.

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