MinT - Information on Result #906303

Information on Result #906303

Linear OOA(4⁶⁷, 45, F₄, 2, 35) (dual of [(45, 2), 23, 36]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(4⁹, 9, F₄, 2, 8) (dual of [(9, 2), 9, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,9P) [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(4¹⁴, 12, F₄, 2, 11) (dual of [(12, 2), 10, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁴, 14, F₄, 2, 11) (dual of [(14, 2), 14, 12]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,16P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
    - an explicitly constructive algebraic function field [i]
linear OOA(4²⁰, 12, F₄, 2, 17) (dual of [(12, 2), 4, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²⁰, 14, F₄, 2, 17) (dual of [(14, 2), 8, 18]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,10P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14 (see above)
linear OOA(4²⁴, 12, F₄, 2, 24) (dual of [(12, 2), 0, 25]-NRT-code), using
- complete OOA / dual of NRT-code with only one code word [i]

Mode: Constructive and linear.

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