MinT - Information on Result #1080640

Information on Result #1080640

Linear OOA(2²⁵⁵, 76, F₂, 4, 105) (dual of [(76, 4), 49, 106]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(2¹⁰⁶, 42, F₂, 4, 52) (dual of [(42, 4), 62, 53]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(4;F,115P) [i] based on function field F/F₂ with g(F) = 54 and N(F) ≥ 42, using
  - an explicitly constructive algebraic function field [i]
linear OOA(2¹⁴⁹, 38, F₂, 4, 105) (dual of [(38, 4), 3, 106]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2¹⁴⁹, 76, F₂, 2, 105) (dual of [(76, 2), 3, 106]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;3,2) [i]
    2. linear OOA(2¹⁴³, 73, F₂, 2, 101) (dual of [(73, 2), 3, 102]-NRT-code), using
      - juxtaposition [i] based on
        linear OOA(2³, 3, F₂, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code) (see above)
        linear OOA(2¹³⁷, 70, F₂, 2, 97) (dual of [(70, 2), 3, 98]-NRT-code), using
        repeating each code word 14 times [i] based on linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
        extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

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None.