MinT - Information on Result #1615589

Information on Result #1615589

Linear OOA(256⁵¹, 582, F₂₅₆, 4, 32) (dual of [(582, 4), 2277, 33]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(256⁵¹, 582, F₂₅₆, 3, 32) (dual of [(582, 3), 1695, 33]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(256⁵¹, 610, F₂₅₆, 3, 32) (dual of [(610, 3), 1779, 33]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(256¹⁷, 289, F₂₅₆, 3, 16) (dual of [(289, 3), 850, 17]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,850P) [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]
  2. linear OOA(256³⁴, 321, F₂₅₆, 3, 32) (dual of [(321, 3), 929, 33]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,930P) [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

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.