MinT - Information on Result #1027767

Information on Result #1027767

Linear OOA(8¹⁶⁸, 57, F₈, 3, 157) (dual of [(57, 3), 3, 158]-NRT-code), using juxtaposition based on

linear OOA(8²¹, 8, F₈, 3, 21) (dual of [(8, 3), 3, 22]-NRT-code), using
- Reedâ€“Solomon NRT-code RS(3;3,8) [i]
linear OOA(8¹⁴⁴, 49, F₈, 3, 135) (dual of [(49, 3), 3, 136]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(8¹⁸, 7, F₈, 3, 18) (dual of [(7, 3), 3, 19]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹⁸, 8, F₈, 3, 18) (dual of [(8, 3), 6, 19]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(3;6,8) [i]
  2. linear OOA(8¹²³, 42, F₈, 3, 116) (dual of [(42, 3), 3, 117]-NRT-code), using
    - repeating each code word 3 times [i] based on linear OOA(8³⁹, 14, F₈, 3, 38) (dual of [(14, 3), 3, 39]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(3;F,3P) [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]

Mode: Constructive and linear.

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