MinT - Information on Result #1027754

Information on Result #1027754

Linear OOA(8¹⁴⁹, 51, F₈, 3, 138) (dual of [(51, 3), 4, 139]-NRT-code), using juxtaposition based on

linear OOA(8³⁸, 14, F₈, 3, 37) (dual of [(14, 3), 4, 38]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(3;F,4P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14, using
  - F₂ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]
linear OOA(8¹⁰⁷, 37, F₈, 3, 100) (dual of [(37, 3), 4, 101]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8³⁵, 13, F₈, 3, 34) (dual of [(13, 3), 4, 35]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8³⁵, 14, F₈, 3, 34) (dual of [(14, 3), 7, 35]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,7P) [i] based on function field F/F₈ with g(F) = 1 and N(F) ≥ 14 (see above)
  2. linear OOA(8⁶⁸, 24, F₈, 3, 65) (dual of [(24, 3), 4, 66]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,6P) [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

Mode: Constructive and linear.

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