MinT - Information on Result #942023

Information on Result #942023

Linear OOA(4²²⁸, 116, F₄, 2, 191) (dual of [(116, 2), 4, 192]-NRT-code), using juxtaposition based on

linear OOA(4²², 13, F₄, 2, 19) (dual of [(13, 2), 4, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4²², 14, F₄, 2, 19) (dual of [(14, 2), 6, 20]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,8P) [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(4²⁰², 103, F₄, 2, 171) (dual of [(103, 2), 4, 172]-NRT-code), using
- juxtaposition [i] based on
  1. 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]
  2. linear OOA(4¹⁸⁴, 94, F₄, 2, 157) (dual of [(94, 2), 4, 158]-NRT-code), using
    - juxtaposition [i] based on
      1. linear OOA(4¹⁴, 9, F₄, 2, 13) (dual of [(9, 2), 4, 14]-NRT-code) (see above)
      2. linear OOA(4¹⁶⁶, 85, F₄, 2, 143) (dual of [(85, 2), 4, 144]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(16¹⁵, 17, F₁₆, 15) (dual of [17, 2, 16]-code or 17-arc in PG(14,16)), using
        extended Reedâ€“Solomon code RS_e(2,16) [i]
        Simplex code S(2,16) [i]
        linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [i]

Mode: Constructive and linear.

None.

None.