MinT - Information on Result #1563856

Information on Result #1563856

Linear OOA(49⁴⁵, 125, F₄₉, 3, 29) (dual of [(125, 3), 330, 30]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(49⁴⁵, 125, F₄₉, 2, 29) (dual of [(125, 2), 205, 30]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(49⁴⁵, 128, F₄₉, 2, 29) (dual of [(128, 2), 211, 30]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(49¹⁵, 64, F₄₉, 2, 14) (dual of [(64, 2), 113, 15]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,113P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(49³⁰, 64, F₄₉, 2, 29) (dual of [(64, 2), 98, 30]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,98P) [i] based on function field F/F₄₉ with g(F) = 1 and N(F) ≥ 64 (see above)

Mode: Linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.