MinT - Information on Result #909862

Information on Result #909862

Linear OOA(4¹⁴², 73, F₄, 2, 113) (dual of [(73, 2), 4, 114]-NRT-code), using juxtaposition based on

linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
  - the Hermitian function field over F₄ [i]
linear OOA(4¹²⁴, 64, F₄, 2, 99) (dual of [(64, 2), 4, 100]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(4¹², 8, F₄, 2, 11) (dual of [(8, 2), 4, 12]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(4¹², 9, F₄, 2, 11) (dual of [(9, 2), 6, 12]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9 (see above)
  2. linear OOA(4¹⁰⁸, 56, F₄, 2, 87) (dual of [(56, 2), 4, 88]-NRT-code), using
    - repeating each code word 4 times [i] based on linear OOA(4²⁴, 14, F₄, 2, 21) (dual of [(14, 2), 4, 22]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,6P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

None.

None.